Princeton University Library Catalog
 Author
 Huber, Annette [Browse]
 Format
 Book
 Language
 English
 Εdition
 1st ed. 2017.
 Published/Created
 Cham : Springer International Publishing : Imprint: Springer, 2017.
 Description
 1 online resource (XXIII, 372 p. 7 illus.)
Details
 Subject(s)

 Author
 Series

 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 65 [More in this series]
 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 00711136 ; 65
 Summary note
 This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori’s abelian category of mixed motives. It develops Nori’s approach to mixed motives from scratch, thereby filling an important gap in the literature, and then explains the connection of mixed motives to periods, including a detailed account of the theory of period numbers in the sense of KontsevichZagier and their structural properties. Period numbers are central to number theory and algebraic geometry, and also play an important role in other fields such as mathematical physics. There are longstanding conjectures about their transcendence properties, best understood in the language of cohomology of algebraic varieties or, more generally, motives. Readers of this book will discover that Nori’s unconditional construction of an abelian category of motives (over fields embeddable into the complex numbers) is particularly well suited for this purpose. Notably, Kontsevich's formal period algebra represents a torsor under the motivic Galois group in Nori's sense, and the period conjecture of Kontsevich and Zagier can be recast in this setting. Periods and Nori Motives is highly informative and will appeal to graduate students interested in algebraic geometry and number theory as well as researchers working in related fields. Containing relevant background material on topics such as singular cohomology, algebraic de Rham cohomology, diagram categories and rigid tensor categories, as well as many interesting examples, the overall presentation of this book is selfcontained.
 Bibliographic references
 Includes bibliographical references and index.
 Contents
 Part I Background Material  General SetUp  Singular Cohomology  Algebraic de Rham Cohomology  Holomorphic de Rham Cohomology  The Period Isomorphism  Categories of (Mixed) Motives  Part II Nori Motives  Nori's Diagram Category  More on Diagrams  Nori Motives  Weights and Pure Nori Motives  Part III Periods  Periods of Varieties  Kontsevich–Zagier Periods  Formal Periods and the Period Conjecture  Part IV Examples  Elementary Examples  Multiple Zeta Values  Miscellaneous Periods: an Outlook.
 ISBN
 9783319509266
 Doi
 10.1007/9783319509266
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