Periods and Nori Motives. 1st ed. 2017

種類:

電子ブック

責任表示:

by Annette Huber, Stefan Müller-Stach

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2017

著者名:

• Huber, Annette.
• Müller-Stach, Stefan.
• SpringerLink (Online service)

シリーズ名:

Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics ; 65

ISBN:

9783319509266 [3319509268]    

注記:

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.
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-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 u

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