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# ðŸ“™ The arithmetic and geometry of algebraic cycles: proceedings of the CRM summer school, June 7-19, 1998, Banff, Alberta, Canada by B. Brent Gordon, James D. Lewis, Stefan MÃ¼ller-Stach, Shuji Saito, Noriko Yui (editors) â€” pdf free

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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 Ã©tale 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.
Titles in this series are co-published with the Centre de Recherches MathÃ©matiques.

## About book:

## About file:

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- Series:
**CRM proceedings & lecture notes #24** - Author:
**B. Brent Gordon, James D. Lewis, Stefan MÃ¼ller-Stach, Shuji Saito, Noriko Yui (editors)** - Year:
**2000** - Publisher:
**American Mathematical Society** - Language:
**English** - ISBN:
**0821819542,9780821819548**

- DPI:
**600** - File size:
**4 196 765** - Format:
**djvu**

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This volume contains the expository lectures and a selection of short communications presented at the Summer School Algebraic and GeometricMethods in Mathematical Physics, held in Kaciveli, Crimea, Ukraine, in September 1993. The contributions, by leading...

The main goal of the CIME Summer School on "Algebraic Cycles and Hodge Theory" has been to gather the most active mathematicians in this area to make the point on the present state of the art. Thus the papers included in the proceedings are surveys and no...

This book is an expanded version of lectures given at a summer school on symplectic geometry in Nordfjordeid, Norway, in June 2001. The unifying feature of the book is an emphasis on Calabi-Yau manifolds. The first part discusses holonomy groups and calib...

This book is based on two series of lectures given at a summer school on algebraic combinatorics at the Sophus Lie Centre in Nordfjordeid, Norway, in June 2003, one by Peter Orlik on hyperplane arrangements, and the other one by Volkmar Welker on free res...

The Pernambuco School on Software Engineering (PSSE) 2004 was the ?rst in a series of events devoted to the study of advanced computer science and to the promotion of international scienti?c collaboration. The main theme in 2004 was re?nement (or rei?cati...

This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009-2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L...

This book constitutes the thoroughly refereed proceedings of the 8th Russian Summer School on Information Retrieval, RuSSIR 2014, held in Nizhniy Novgorod, Russia, in August 2014.The volume includes 6 tutorial papers, summarizing lectures given at the eve...

This book constitutes the thoroughly refereed proceedings of the 9th Russian Summer School on Information Retrieval, RuSSIR 2015, held in Saint Petersburg, Russia, in August 2015.The volume includes 5 tutorial papers, summarizing lectures given at the eve...

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Design and Simulate Any Type of CMOS Circuit!Electronic circuit designers and electronic engineering students can turn to Basics of CMOS Cell Design for a practice-based introduction to the design and simulation of every major type of CMOS (complementary ...

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