Annette Huber

(Author)

Periods and Nori Motives (Softcover Reprint of the Original 1st 2017)Paperback - Softcover Reprint of the Original 1st 2017, 21 July 2018

Periods and Nori Motives (Softcover Reprint of the Original 1st 2017)
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Part of Series
Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge /
Print Length
372 pages
Language
English
Publisher
Springer
Date Published
21 Jul 2018
ISBN-10
3319845241
ISBN-13
9783319845241

Description

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 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.

Product Details

Authors:
Annette HuberStefan Müller-Stach
Book Edition:
Softcover Reprint of the Original 1st 2017
Book Format:
Paperback
Country of Origin:
NL
Date Published:
21 July 2018
Dimensions:
23.39 x 15.6 x 2.08 cm
ISBN-10:
3319845241
ISBN-13:
9783319845241
Language:
English
Location:
Cham
Pages:
372
Publisher:
Weight:
553.38 gm

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