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  1. Transcendence and linear relations of 1-periods
    Author: Huber, Annette; Wüstholz, Gisbert
    Published: 2022
    Publisher:  Cambridge University Press, Cambridge

    Location:
    Bibliothek des Fachbereichs Mathematik und Informatik der Universität
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    Hube / 41341
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    Universitätsbibliothek Trier
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    XB/c18125-227
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    Source: Union catalogues
    Language: English
    Media type: Book
    ISBN: 9781316519936
    Other identifier:
    Series: Cambridge tracts in mathematics ; 227
    Subjects: Kategorientheorie; Transzendente Zahl; Motiv <Mathematik>; Kohomologie; Gruppentheorie
    Other subjects: Transcendental numbers; Motives (Mathematics); Algebraic fields; MATHEMATICS / Number Theory
    Scope: xx, 243 Seiten, Illustrationen
  2. Lectures on the theory of pure motives
    Author: Murre, Jacob P.; Nagel, Jan; Peters, Chris
    Published: [2013]; © 2013
    Publisher:  American Mathematical Society, Providence, Rhode Island

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    Universitätsbibliothek Bielefeld
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    Volltext (URL des Erstveröffentlichers)
    Source: Union catalogues
    Language: English
    Media type: Ebook
    Format: Online
    ISBN: 9781470410391
    Other identifier:
    RVK Categories: SI 165 ; SK 320
    Series: University lecture series ; volume 61
    Subjects: Motives (Mathematics); Algebraic geometry -- Cycles and subschemes -- (Equivariant) Chow groups and rings; motives; Algebraic geometry -- Cycles and subschemes -- Algebraic cycles; Commutative algebra -- Homological methods -- Grothendieck groups, K-theory; Motiv <Mathematik>
    Scope: 1 Online-Ressource (ix, 149 Seiten), Diagramme
  3. Mixed motives
    Author: Levine, Marc
    Published: 1998
    Publisher:  American Mathematical Society, Providence, RI

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    Staatsbibliothek zu Berlin - Preußischer Kulturbesitz, Haus Unter den Linden
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    Source: Staatsbibliothek zu Berlin
    Language: English
    Media type: Book
    Format: Print
    ISBN: 0821807854
    Other identifier:
    9780821807859
    RVK Categories: SK 300
    Series: Mathematical surveys and monographs ; 57
    Subjects: Homology theory; Motives (Mathematics)
    Other subjects: Motives (Mathematics)
    Scope: X, 515 S, 27 cm
    Notes:

    Includes bibliographical references (p. 501 - 506) and indexes
  4. Mixed motives and their realization in derived categories
    Author: Huber, Annette
    Published: 1995
    Publisher:  Springer, Berlin u.a.

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    Universitätsbibliothek Eichstätt-Ingolstadt
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    Source: Union catalogues
    Language: German
    Media type: Book
    ISBN: 3540594752
    RVK Categories: SI 850 ; SK 320
    Series: Lecture notes in mathematics ; 1604
    Subjects: Homology theory; Motives (Mathematics); Motiv <Mathematik>; Kategorie <Mathematik>; Kohomologie
    Scope: XV, 207 S.
  5. Feynman motives
    Author: Marcolli, Matilde
    Published: c2010
    Publisher:  World Scientific, Hackensack, N.J.

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    Source: Union catalogues
    Language: English
    Media type: Ebook
    Format: Online
    ISBN: 9789814271219
    RVK Categories: SK 950
    Subjects: Feynman integrals; Motives (Mathematics); Quantum field theory; Quantenfeldtheorie; Algebraische Varietät; Motiv <Mathematik>; Pfadintegral
    Scope: xiii, 220 p.
    Notes:

    Includes bibliographical references and index
  6. Noncommutative motives
    Author: Tabuada, Gonçalo
    Published: [2015]; © 2015
    Publisher:  American Mathematical Society, Providence, Rhode Island

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    Universitätsbibliothek der LMU München
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    Volltext (URL des Erstveröffentlichers)
    Source: Union catalogues
    Language: English
    Media type: Ebook
    Format: Online
    ISBN: 9781470426279
    Other identifier:
    RVK Categories: SI 165 ; SK 240 ; SK 320
    Series: University Lecture Series / American Mathematical Society ; Volume 63
    Subjects: Motives (Mathematics); Nichtkommutative Geometrie; Motiv <Mathematik>
    Scope: 1 Online-Ressource (x, 114 Seiten)
  7. Feynman motives
    Author: Marcolli, Matilde
    Published: c2010
    Publisher:  World Scientific Pub. Co., Singapore

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    Ostbayerische Technische Hochschule Amberg-Weiden / Hochschulbibliothek Amberg
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    Ostbayerische Technische Hochschule Amberg-Weiden, Hochschulbibliothek, Standort Weiden
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    Source: Union catalogues
    Language: English
    Media type: Ebook
    Format: Online
    ISBN: 9789814271202; 9789814271219; 9814271209; 9814271217
    RVK Categories: SK 950
    Subjects: MATHEMATICS / Geometry / Algebraic; Algebraische Varietät; Motiv (Mathematik); Pfadintegral; Quantenfeldtheorie; Feynman integrals; Motives (Mathematics); Quantum field theory; Motives (Mathematics); Feynman integrals; Quantum field theory; Quantenfeldtheorie; Algebraische Varietät; Motiv <Mathematik>; Pfadintegral
    Scope: 1 Online-Ressource (xiii, 220 p.)
    Notes:

    Includes bibliographical references (p. 207-213) and index

    1. Perturbative quantum field theory and Feynman diagrams. 1.1. A calculus exercise in Feynman integrals. 1.2. From Lagrangian to effective action. 1.3. Feynman rules. 1.4. Simplifying graphs : vacuum bubbles, connected graphs. 1.5. One-particle-irreducible graphs. 1.6. The problem of renormalization. 1.7. Gamma functions, Schwinger and Feynman parameters. 1.8. Dimensional regularization and minimal subtraction -- 2. Motives and periods. 2.1. The idea of motives. 2.2. Pure motives. 2.3. Mixed motives and triangulated categories. 2.4. Motivic sheaves. 2.5. The Grothendieck ring of motives. 2.6. Tate motives. 2.7. The algebra of periods. 2.8. Mixed Tate motives and the logarithmic extensions. 2.9. Categories and Galois groups. 2.10. Motivic Galois groups --

    - 3. Feynman integrals and algebraic varieties. 3.1. The parametric Feynman integrals. 3.2. The graph hypersurfaces. 3.3. Landau varieties. 3.4. Integrals in affine and projective spaces. 3.5. Non-isolated singularities. 3.6. Cremona transformation and dual graphs. 3.7. Classes in the Grothendieck ring. 3.8. Motivic Feynman rules. 3.9. Characteristic classes and Feynman rules. 3.10. Deletion-contraction relation. 3.11. Feynman integrals and periods. 3.12. The mixed Tate mystery. 3.13. From graph hypersurfaces to determinant hypersurfaces. 3.14. Handling divergences. 3.15. Motivic zeta functions and motivic Feynman rules -- 4. Feynman integrals and Gelfand-Leray forms. 4.1. Oscillatory integrals. 4.2. Leray regularization of Feynman integrals --

    - 5. Connes-Kreimer theory in a nutshell. 5.1. The Bogolyubov recursion. 5.2. Hopf algebras and affine group schemes. 5.3. The Connes-Kreimer Hopf algebra. 5.4. Birkhoff factorization. 5.5. Factorization and Rota-Baxter algebras. 5.6. Motivic Feynman rules and Rota-Baxter structure -- 6. The Riemann-Hilbert correspondence. 6.1. From divergences to iterated integrals. 6.2. From iterated integrals to differential systems. 6.3. Flat equisingular connections and vector bundles. 6.4. The "cosmic Galois group" -- 7. The geometry of DimReg. 7.1. The motivic geometry of DimReg. 7.2. The noncommutative geometry of DimReg -- 8. Renormalization, singularities, and Hodge structures. 8.1. Projective radon transform. 8.2. The polar filtration and the Milnor fiber. 8.3. DimReg and mixed Hodge structures. 8.4. Regular and irregular singular connections --

    - 9. Beyond scalar theories. 9.1. Supermanifolds. 9.2. Parametric Feynman integrals and supermanifolds. 9.3. Graph supermanifolds. 9.4. Noncommutative field theories

    This book presents recent and ongoing research work aimed at understanding the mysterious relation between the computations of Feynman integrals in perturbative quantum field theory and the theory of motives of algebraic varieties and their periods. One of the main questions in the field is understanding when the residues of Feynman integrals in perturbative quantum field theory evaluate to periods of mixed Tate motives. The question originates from the occurrence of multiple zeta values in Feynman integrals calculations observed by Broadhurst and Kreimer. Two different approaches to the subject are described. The first, a "bottom-up" approach, constructs explicit algebraic varieties and periods from Feynman graphs and parametric Feynman integrals.

    This approach, which grew out of work of Bloch-Esnault-Kreimer and was more recently developed in joint work of Paolo Aluffi and the author, leads to algebro-geometric and motivic versions of the Feynman rules of quantum field theory and concentrates on explicit constructions of motives and classes in the Grothendieck ring of varieties associated to Feynman integrals. While the varieties obtained in this way can be arbitrarily complicated as motives, the part of the cohomology that is involved in the Feynman integral computation might still be of the special mixed Tate kind. A second, "top-down" approach to the problem, developed in the work of Alain Connes and the author, consists of comparing a Tannakian category constructed out of the data of renormalization of perturbative scalar field theories, obtained in the form of a Riemann-Hilbert correspondence, with Tannakian categories of mixed Tate motives.

    The book draws connections between these two approaches and gives an overview of other ongoing directions of research in the field, outlining the many connections of perturbative quantum field theory and renormalization to motives, singularity theory, Hodge structures, arithmetic geometry, supermanifolds, algebraic and non-commutative geometry. The text is aimed at researchers in mathematical physics, high energy physics, number theory and algebraic geometry. Partly based on lecture notes for a graduate course given by the author at Caltech in the fall of 2008, it can also be used by graduate students interested in working in this area
  8. Feynman motives
    Author: Marcolli, Matilde
    Published: c2010
    Publisher:  World Scientific Pub. Co., Singapore

    The book draws connections between these two approaches and gives an overview of other ongoing directions of research in the field, outlining the many connections of perturbative quantum field theory and renormalization to motives, singularity... more

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    Technische Hochschule Nürnberg Georg Simon Ohm, Bibliothek
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    The book draws connections between these two approaches and gives an overview of other ongoing directions of research in the field, outlining the many connections of perturbative quantum field theory and renormalization to motives, singularity theory, Hodge structures, arithmetic geometry, supermanifolds, algebraic and non-commutative geometry. The text is aimed at researchers in mathematical physics, high energy physics, number theory and algebraic geometry. Partly based on lecture notes for a graduate course given by the author at Caltech in the fall of 2008, it can also be used by graduate students interested in working in this area

     
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    Volltext (URL des Erstveroeffentlichers)
    Source: Union catalogues
    Language: English
    Media type: Ebook
    Format: Online
    ISBN: 9789814271219
    Other identifier:
    RVK Categories: SK 950
    Subjects: Motives (Mathematics); Feynman integrals; Quantum field theory; Algebraische Varietät; Pfadintegral; Quantenfeldtheorie; Motiv <Mathematik>
    Scope: xiii, 220 p., ill
  9. Feynman motives
    Author: Marcolli, Matilde
    Published: c2010
    Publisher:  World Scientific, Hackensack, N.J.

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    Source: Union catalogues
    Language: English
    Media type: Ebook
    Format: Online
    ISBN: 9789814271219
    RVK Categories: SK 950
    Subjects: Feynman integrals; Motives (Mathematics); Quantum field theory; Quantenfeldtheorie; Algebraische Varietät; Motiv <Mathematik>; Pfadintegral
    Scope: xiii, 220 p.
    Notes:

    Includes bibliographical references and index
  10. Lectures on the theory of pure motives
    Author: Murre, Jacob P.; Nagel, Jan; Peters, Chris
    Published: [2013]; © 2013
    Publisher:  American Mathematical Society, Providence, Rhode Island

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    Universitätsbibliothek der LMU München
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    Universitätsbibliothek Regensburg
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    Source: Union catalogues
    Language: English
    Media type: Ebook
    Format: Online
    ISBN: 9781470410391
    Other identifier:
    RVK Categories: SI 165 ; SK 320 ; SK 240
    Series: University lecture series ; Volume 61
    Subjects: Motives (Mathematics); Algebraic geometry -- Cycles and subschemes -- (Equivariant) Chow groups and rings; motives; Algebraic geometry -- Cycles and subschemes -- Algebraic cycles; Commutative algebra -- Homological methods -- Grothendieck groups, K-theory; Motiv <Mathematik>
    Scope: 1 Online-Ressource (ix, 149 Seiten), Diagramme
  11. Motives and algebraic cycles
    a celebration in honour of Spencer J. Bloch
    Published: 2009
    Publisher:  American Mathematical Society, Providence, R.I.

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    Universitätsbibliothek Augsburg
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    Universitätsbibliothek Regensburg
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    Source: Union catalogues
    Language: English
    Media type: Book
    ISBN: 9780821844946; 0821844946
    RVK Categories: SK 230
    Series: Fields Institute communications ; 56
    Subjects: Algebraic cycles; Motives (Mathematics); Motiv <Mathematik>; Algebraische Zykel
    Scope: VIII, 336 S.
    Notes:

    Includes bibliographical references
  12. Lectures on the theory of pure motives
    Author: Murre, Jacob P.; Nagel, Jan; Peters, Chris
    Published: [2013]; © 2013
    Publisher:  American Mathematical Society, Providence, Rhode Island

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    Universitätsbibliothek Bayreuth
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    Technische Universität München, Universitätsbibliothek, Teilbibliotheken Garching
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    Universitätsbibliothek der LMU München
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  13. Une introduction aux motifs
    (motifs purs, motifs mixtes, périodes)
    Author: André, Yves
    Published: 2004
    Publisher:  Société Mathématique de France, Paris

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    Universitätsbibliothek Erlangen-Nürnberg, Technisch-naturwissenschaftliche Zweigbibliothek
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    Universitätsbibliothek der LMU München
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    Source: Union catalogues
    Language: French
    Media type: Book
    ISBN: 2856291643
    RVK Categories: SI 693
    Series: Panoramas et synthèses ; 17
    Subjects: Cohomologie; Motif (Mathématiques); Motives (Mathematics); Motiv <Mathematik>
    Scope: XI, 261 S., graph. Darst.
    Notes:

    Literaturverz. S. [245] - 258
  14. Feynman motives
    Author: Marcolli, Matilde
    Published: 2010
    Publisher:  World Scientific, New Jersey [u.a.]

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    Universitätsbibliothek Erlangen-Nürnberg, Technisch-naturwissenschaftliche Zweigbibliothek
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    Source: Union catalogues
    Language: English
    Media type: Book
    ISBN: 9789814271202; 9814271209; 9789814304481; 9814304484
    RVK Categories: SK 950
    Subjects: Feynman integrals; Motives (Mathematics); Quantum field theory; Pfadintegral; Algebraische Varietät; Quantenfeldtheorie; Motiv <Mathematik>
    Scope: XIII, 220 S., graph. Darst.
  15. Kummer-Chern-Eisenstein motives via Hilbert modular surfaces
    Author: Caspar, Alexander
    Published: 2003
    Publisher:  Math.-Naturwiss. Fak. der Rheinischen Friedrich-Wilhelms-Univ., Bonn

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    Staatsbibliothek zu Berlin - Preußischer Kulturbesitz, Haus Potsdamer Straße
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    5 Bon 20 / 358
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    Technische Informationsbibliothek (TIB) / Leibniz-Informationszentrum Technik und Naturwissenschaften und Universitätsbibliothek
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    RA 224(358)
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    Universitätsbibliothek Osnabrück
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    Universitätsbibliothek Rostock
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    Source: Staatsbibliothek zu Berlin
    Language: English
    Media type: Dissertation
    Format: Print
    RVK Categories: SI 180
    Series: Bonner mathematische Schriften ; 358
    Subjects: Hilbert modular surfaces; Motives (Mathematics)
    Scope: 100 S, graph. Darst, 21 cm
    Notes:

    Zugl.: Bonn, Univ., Diss., 2003
  16. Kummer-Chern-Eisenstein motives via Hilbert modular surfaces
    Author: Caspar, Alexander
    Published: 2003
    Publisher:  Math. Inst. der Univ., Bonn

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    Universitätsbibliothek Bayreuth
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    Universitätsbibliothek Erlangen-Nürnberg, Technisch-naturwissenschaftliche Zweigbibliothek
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    Technische Universität München, Universitätsbibliothek, Teilbibliotheken Garching
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    Source: Union catalogues
    Language: English
    Media type: Dissertation
    RVK Categories: SI 180
    Series: Bonner mathematische Schriften ; 358
    Subjects: Hilbert modular surfaces; Motives (Mathematics); Motiv <Mathematik>; Kohomologie; Hilbertsche Modulfläche
    Scope: 100 S.
    Notes:

    Bonn, Univ., Diss., 2003
  17. Lectures on the theory of pure motives
    Author: Murre, Jacob P; Nagel, Jan; Peters, Chris
    Published: [2013]; © 2013
    Publisher:  American Mathematical Society, Providence, Rhode Island

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    Universitätsbibliothek Bielefeld
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    Source: Union catalogues
    Language: English
    Media type: Ebook
    Format: Online
    ISBN: 9781470410391
    Other identifier:
    RVK Categories: SI 165 ; SK 320
    Series: University lecture series ; volume 61
    Subjects: Motives (Mathematics); Algebraic geometry -- Cycles and subschemes -- (Equivariant) Chow groups and rings; motives; Algebraic geometry -- Cycles and subschemes -- Algebraic cycles; Commutative algebra -- Homological methods -- Grothendieck groups, ¤K¤-theory
    Scope: 1 Online-Ressource (ix, 149 Seiten), Diagramme
  18. Lectures on the theory of pure motives
    Author: Murre, Jacob P.; Nagel, Jan; Peters, Chris A.
    Published: 2013
    Publisher:  American Math. Soc., Providence, RI

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    Universität Potsdam, Universitätsbibliothek
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    Source: Union catalogues
    Language: English
    Media type: Book
    Format: Print
    ISBN: 9780821894347
    Other identifier:
    9780821894347
    RVK Categories: SI 165
    Series: University lecture series ; 61
    Subjects: Motives (Mathematics)
    Scope: IX, 149 S., 25 cm
    Notes:

    Includes bibliographical references (pages 139 - 144) and indexes
  19. Lectures on the theory of pure motives
    Author: Murre, Jacob P.; Nagel, Jan; Peters, Chris
    Published: [2013]; © 2013
    Publisher:  American Mathematical Society, Providence, Rhode Island

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    Freie Universität Berlin, Universitätsbibliothek
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    Humboldt-Universität zu Berlin, Universitätsbibliothek, Jacob-und-Wilhelm-Grimm-Zentrum
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    Universität Potsdam, Universitätsbibliothek
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  20. Motives, quantum field theory, and pseudodifferential operators
    Contributor: Carey, Alan L. (Publisher)
    Published: 2010
    Publisher:  American Math. Soc. [u.a.], Providence, RI

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    Source: Union catalogues
    Contributor: Carey, Alan L. (Publisher)
    Language: English
    Media type: Book
    Format: Print
    ISBN: 9780821851999
    Series: Clay mathematics proceedings ; 12
    Subjects: Geometry, Algebraic; Motives (Mathematics); Quantum theory; Pseudodifferential operators
    Scope: X, 349 S., graph. Darst.
    Notes:

    Literaturangaben
  21. Motives and algebraic cycles
    a celebration in honour of Spencer J. Bloch
    Contributor: Jeu, Rob <<de>> (Publisher); Bloch, Spencer
    Published: 2009
    Publisher:  American Math. Soc. [u.a.], Providence, RI

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    Source: Union catalogues
    Contributor: Jeu, Rob <<de>> (Publisher); Bloch, Spencer
    Language: English
    Media type: Book
    Format: Print
    ISBN: 9780821844946
    RVK Categories: SK 230
    Series: Fields Institute communications ; 56
    Subjects: Algebraic cycles; Motives (Mathematics)
    Scope: XI, 336 S., graph. Darst.
    Notes:

    Literaturangaben
  22. Feynman motives
    Author: Marcolli, Matilde
    Published: 2010
    Publisher:  World Scientific, New Jersey [u.a.]

    Location:
    Humboldt-Universität zu Berlin, Universitätsbibliothek, Jacob-und-Wilhelm-Grimm-Zentrum
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    Language: English
    Media type: Book
    ISBN: 9789814271202; 9814271209; 9789814304481; 9814304484
    RVK Categories: SK 950
    Subjects: Feynman integrals; Motives (Mathematics); Quantum field theory; Pfadintegral; Algebraische Varietät; Quantenfeldtheorie; Motiv <Mathematik>
    Scope: XIII, 220 S., graph. Darst.
  23. Lectures on the theory of pure motives
    Author: Murre, Jacob P.; Nagel, Jan; Peters, Chris
    Published: [2013]; © 2013
    Publisher:  American Mathematical Society, Providence, Rhode Island

    Location:
    Humboldt-Universität zu Berlin, Universitätsbibliothek, Jacob-und-Wilhelm-Grimm-Zentrum
    Inter-library loan:
    Unlimited inter-library loan, copies and loan

    Location:
    TU Berlin, Universitätsbibliothek
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    Unlimited inter-library loan, copies and loan
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    Content information
    Volltext (URL des Erstveröffentlichers)
    Source: Union catalogues
    Language: English
    Media type: Ebook
    Format: Online
    ISBN: 9781470410391
    Other identifier:
    RVK Categories: SI 165 ; SK 320 ; SK 240
    Series: University lecture series ; Volume 61
    Subjects: Motives (Mathematics); Algebraic geometry -- Cycles and subschemes -- (Equivariant) Chow groups and rings; motives; Algebraic geometry -- Cycles and subschemes -- Algebraic cycles; Commutative algebra -- Homological methods -- Grothendieck groups, K-theory; Motiv <Mathematik>
    Scope: 1 Online-Ressource (ix, 149 Seiten), Diagramme
  24. Motives and algebraic cycles
    a celebration in honour of Spencer J. Bloch
    Contributor: Bloch, Spencer (MitwirkendeR); Jeu, Rob de (MitwirkendeR); Lewis, James Dominic (MitwirkendeR)
    Published: 2009
    Publisher:  American Mathematical Society, Providence, R.I

    Location:
    Mathematisches Forschungsinstitut Oberwolfach gGmbH, Bibliothek
    Signature:
    eBook
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    Source: Union catalogues
    Contributor: Bloch, Spencer (MitwirkendeR); Jeu, Rob de (MitwirkendeR); Lewis, James Dominic (MitwirkendeR)
    Language: English
    Media type: Ebook
    Format: Online
    ISBN: 9781470417833
    RVK Categories: SK 230
    Edition: Online-Ausg.
    Series: Fields Institute Communications ; v. 56
    AMS ebook collection
    Subjects: Algebraic cycles; Motives (Mathematics)
    Scope: Online-Ressource (1 online resource (xi, 336 p. : ill.))
    Notes:

    Includes bibliographical references. - Electronic reproduction; Providence, Rhode Island; American Mathematical Society; 2012. - Description based on print version record
  25. Mixed motives
    Author: Levine, Marc
    Published: 1998
    Publisher:  American Mathematical Society, Providence, R.I

    Location:
    Niedersächsische Staats- und Universitätsbibliothek Göttingen
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    Location:
    Mathematisches Forschungsinstitut Oberwolfach gGmbH, Bibliothek
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    Location:
    Universitätsbibliothek Rostock
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    Source: Union catalogues
    Language: English
    Media type: Ebook
    Format: Online
    ISBN: 9780821833988
    RVK Categories: SK 300
    Edition: Online-Ausg.
    Series: Mathematical Surveys and Monographs 0076-5376 (print) 2331-7159 (online) ; v. 57
    Subjects: Motives (Mathematics); Homology theory; Motives (Mathematics)
    Scope: Online-Ressource (1 online resource (x, 515 p.))
    Notes:

    Includes bibliographical references (p. 501-506) and indexes. - Electronic reproduction; Providence, Rhode Island; American Mathematical Society; 2012. - Description based on print version record