Arithmetic and Geometry of Algebraic Cycles
Arithmetic and Geometry of Algebraic Cycles
Arithmetic and Geometry of Algebraic Cycles
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Type: eBook
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Publisher: American Mathematical Society
Page Count: 230
Format: djvu
Language: English
ISBN-10: 0821819542
ISBN-13: 9780821819548
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Free Arithmetic and Geometry of Algebraic Cycles pdf


Ebook B. Brent Gordon, James D. Lewis, Noriko Yui, Shuji Saito, Stefan Müller-Stach epub


The NATO ASI/CRM Summer School at Banff offered a unique, full, and in-depth account of the topic, ranging from introductory courses by leading experts to discussions of the latest developments by all participants. The papers have been organized into three categories: cohomological methods; Chow groups and motives; and arithmetic methods.

As a subfield of algebraic geometry, the theory of algebraic cycles has gone through various interactions with algebraic $K$-theory, Hodge theory, arithmetic algebraic geometry, number theory, and topology. These interactions have led to developments such as a description of Chow groups in terms of algebraic $K$-theory, the application of the Merkurjev-Suslin theorem to the arithmetic Abel-Jacobi mapping, progress on the celebrated conjectures of Hodge, and of Tate, which compute cycles class groups respectively in terms of Hodge theory or as the invariants of a Galois group action on étale cohomology, the conjectures of Bloch and Beilinson, which explain the zero or pole of the $L$-function of a variety and interpret the leading non-zero coefficient of its Taylor expansion at a critical point, in terms of arithmetic and geometric invariant of the variety and its cycle class groups.

The immense recent progress in the theory of algebraic cycles is based on its many interactions with several other areas of mathematics. This conference was the first to focus on both arithmetic and geometric aspects of algebraic cycles. It brought together leading experts to speak from their various points of view. A unique opportunity was created to explore and view the depth and the breadth of the subject. This volume presents the intriguing results.


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collection of surveys

This book is a collection of survey articles on the subject of algebraic cycles and motivic cohomology based on the NATO conference on algebraic cycles held at Banff, Canada. Survey papers contained in this book will definitely tell you what you need to know and where you should go to pursue research in this area. Libraries in major universities will definitely have this very important collection, but, if for algebraic geometers who work on algebraic cycles, having this book can be very convenient for their personal usage.

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