Overview
- First book presenting the theory of Nori motives in detail
- Studies the Kontsevich–Zagier theory of periods and its relation to mixed motives
- Includes full background as well as many examples
- Includes supplementary material: sn.pub/extras
Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (MATHE3, volume 65)
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Table of contents (16 chapters)
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Front Matter
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Background Material
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Front Matter
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Nori Motives
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Front Matter
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Periods
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Front Matter
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Examples
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Front Matter
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Keywords
About this book
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 long-standing 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 self-contained.
Reviews
“The book under review provides a detailed account on some of the theory of so-called Nori motives … . The authors provide a lot of details and background information, making this book very accessible. … this book is a valuable contribution to the field of motives. Particularly commendable is the attention to detail, which can sometimes be missing in this field riddled with conjectures and folklore results. The expository nature makes this book useful to a wide audience.” (Tom Bachmann, zbMATH 1369.14001, 2017)
“This text is both a stimulating introduction and a sound comprehensive reference for anyone interested in the field of motives and periods. … All things considered, I strongly feel that the authors deserve praise for their valiant work. They have fulfilled their difficult program bravely and efficiently.” (Alberto Collino, Mathematical Reviews, 2017)
Authors and Affiliations
About the authors
Stefan Müller-Stach works in algebraic geometry, focussing on algebraic cycles, regulators and period integrals. His work includes the detection of classes in motivic cohomology via regulators and the study of special subvarieties in Mumford-Tate varieties. More recent research interests include periods and their relations to mathematical physics and foundations of mathematics.
Bibliographic Information
Book Title: Periods and Nori Motives
Authors: Annette Huber, Stefan Müller-Stach
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
DOI: https://doi.org/10.1007/978-3-319-50926-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-50925-9Published: 20 March 2017
Softcover ISBN: 978-3-319-84524-1Published: 21 July 2018
eBook ISBN: 978-3-319-50926-6Published: 08 March 2017
Series ISSN: 0071-1136
Series E-ISSN: 2197-5655
Edition Number: 1
Number of Pages: XXIII, 372
Number of Illustrations: 7 b/w illustrations
Topics: Number Theory, Algebraic Geometry, K-Theory, Algebraic Topology, Category Theory, Homological Algebra, Associative Rings and Algebras