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CLC: O - 数理科学和化学

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Periods and Nori Motives /

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...

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Bibliographic Details
Main Authors: Huber, Annette
Corporate Authors: SpringerLink Online service
Group Author: M ller-Stach, Stefan
Published: Springer International Publishing : Imprint: Springer,
Publisher Address: Cham :
Publication Dates: 2017.
Literature type: eBook
Language: English
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 65
Subjects:
Mathematics
Algebraic geometry
Associative rings
Rings Algebra
Category theory Mathematics
Homological algebra
K-theory
Number theory
Algebraic topology
Category Theory, Homological Algebra
Associative Rings and Algebras
Online Access: http://dx.doi.org/10.1007/978-3-319-50926-6
Summary: 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 Kontsevich-Zagier 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 long-
Carrier Form: 1 online resource (XXIII, 372 pages) : illustrations.
ISBN: 9783319509266
Index Number: QA241
CLC: O156
Contents: Part I Background Material -- General Set-Up -- 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.

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