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Algebraic cycles and motives
Authors: ---
ISBN: 9780521701754 9781107325968 9781107089327 1107089328 110732596X 9780521701747 0521701740 0521701759 1139882716 1107101174 1107103649 1107092299 1107095611 Year: 2007 Volume: 344 Publisher: Cambridge : Cambridge University Press,

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Abstract

Algebraic geometry is a central subfield of mathematics in which the study of cycles is an important theme. Alexander Grothendieck taught that algebraic cycles should be considered from a motivic point of view and in recent years this topic has spurred a lot of activity. This book is one of two volumes that provide a self-contained account of the subject as it stands. Together, the two books contain twenty-two contributions from leading figures in the field which survey the key research strands and present interesting new results. Topics discussed include: the study of algebraic cycles using Abel-Jacobi/regulator maps and normal functions; motives (Voevodsky's triangulated category of mixed motives, finite-dimensional motives); the conjectures of Bloch-Beilinson and Murre on filtrations on Chow groups and Bloch's conjecture. Researchers and students in complex algebraic geometry and arithmetic geometry will find much of interest here.

Algebraic cycles and motives.
Authors: --- ---
ISBN: 9780511721496 9780521701747 9781107362987 1107362989 9780511893926 0511893922 0511721498 0521701740 1139882708 9781139882705 1107367891 9781107367890 1107372437 9781107372436 1107369924 9781107369924 1299405495 9781299405493 1107365430 9781107365438 Year: 2007 Publisher: Cambridge, U.K. : Cambridge University Press,

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Abstract

Algebraic geometry is a central subfield of mathematics in which the study of cycles is an important theme. Alexander Grothendieck taught that algebraic cycles should be considered from a motivic point of view and in recent years this topic has spurred a lot of activity. This 2007 book is one of two volumes that provide a self-contained account of the subject. Together, the two books contain twenty-two contributions from leading figures in the field which survey the key research strands and present interesting new results. Topics discussed include: the study of algebraic cycles using Abel-Jacobi/regulator maps and normal functions; motives (Voevodsky's triangulated category of mixed motives, finite-dimensional motives); the conjectures of Bloch-Beilinson and Murre on filtrations on Chow groups and Bloch's conjecture. Researchers and students in complex algebraic geometry and arithmetic geometry will find much of interest here.


Book
Feynman motives
Author:
ISBN: 128275789X 9786612757891 9814271217 9789814271219 9814271209 9789814271202 9814304484 9789814304481 Year: 2010 Publisher: Hackensack, N.J. World Scientific

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Abstract

Presents the research work aimed at understanding the mysterious relation between the computations of Feynman integrals in perturbative quantum field theory and the theory of motives of algebraic varieties and their periods.


Book
Motivic Integration
Authors: --- ---
ISBN: 9781493978878 9781493978854 1493978853 149397887X Year: 2018 Publisher: New York, NY : Springer New York : Imprint: Birkhäuser,

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Abstract

This monograph focuses on the geometric theory of motivic integration, which takes its values in the Grothendieck ring of varieties. This theory is rooted in a groundbreaking idea of Kontsevich and was further developed by Denef & Loeser and Sebag. It is presented in the context of formal schemes over a discrete valuation ring, without any restriction on the residue characteristic. The text first discusses the main features of the Grothendieck ring of varieties, arc schemes, and Greenberg schemes. It then moves on to motivic integration and its applications to birational geometry and non-Archimedean geometry. Also included in the work is a prologue on p-adic analytic manifolds, which served as a model for motivic integration. With its extensive discussion of preliminaries and applications, this book is an ideal resource for graduate students of algebraic geometry and researchers of motivic integration. It will also serve as a motivation for more recent and sophisticated theories that have been developed since. .

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