Periods and Nori Motives

Nonfiction, Science & Nature, Mathematics, Number Theory, Geometry
Cover of the book Periods and Nori Motives by Annette Huber, Benjamin Friedrich, Jonas von Wangenheim, Stefan Müller-Stach, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Annette Huber, Benjamin Friedrich, Jonas von Wangenheim, Stefan Müller-Stach ISBN: 9783319509266
Publisher: Springer International Publishing Publication: March 8, 2017
Imprint: Springer Language: English
Author: Annette Huber, Benjamin Friedrich, Jonas von Wangenheim, Stefan Müller-Stach
ISBN: 9783319509266
Publisher: Springer International Publishing
Publication: March 8, 2017
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book HRM in Mission Driven Organizations by Annette Huber, Benjamin Friedrich, Jonas von Wangenheim, Stefan Müller-Stach
Cover of the book Advances in Italian Mechanism Science by Annette Huber, Benjamin Friedrich, Jonas von Wangenheim, Stefan Müller-Stach
Cover of the book Genetic Programming Theory and Practice XIII by Annette Huber, Benjamin Friedrich, Jonas von Wangenheim, Stefan Müller-Stach
Cover of the book Finding Solutions for Protecting and Sharing Archaeological Heritage Resources by Annette Huber, Benjamin Friedrich, Jonas von Wangenheim, Stefan Müller-Stach
Cover of the book Synthetic Biology Analysed by Annette Huber, Benjamin Friedrich, Jonas von Wangenheim, Stefan Müller-Stach
Cover of the book Intelligent Interactive Multimedia Systems and Services in Practice by Annette Huber, Benjamin Friedrich, Jonas von Wangenheim, Stefan Müller-Stach
Cover of the book Principles and Applications of Aggregation-Induced Emission by Annette Huber, Benjamin Friedrich, Jonas von Wangenheim, Stefan Müller-Stach
Cover of the book Statistics for Mathematicians by Annette Huber, Benjamin Friedrich, Jonas von Wangenheim, Stefan Müller-Stach
Cover of the book Quantum Theory and Statistical Thermodynamics by Annette Huber, Benjamin Friedrich, Jonas von Wangenheim, Stefan Müller-Stach
Cover of the book Electrospun Biomaterials and Related Technologies by Annette Huber, Benjamin Friedrich, Jonas von Wangenheim, Stefan Müller-Stach
Cover of the book Neo-Tribes by Annette Huber, Benjamin Friedrich, Jonas von Wangenheim, Stefan Müller-Stach
Cover of the book Asian American Parenting by Annette Huber, Benjamin Friedrich, Jonas von Wangenheim, Stefan Müller-Stach
Cover of the book The Political Discourse of Spatial Disparities by Annette Huber, Benjamin Friedrich, Jonas von Wangenheim, Stefan Müller-Stach
Cover of the book Lacan and the Nonhuman by Annette Huber, Benjamin Friedrich, Jonas von Wangenheim, Stefan Müller-Stach
Cover of the book Notes on the Infinity Laplace Equation by Annette Huber, Benjamin Friedrich, Jonas von Wangenheim, Stefan Müller-Stach
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy