Andrei Suslin's Books

Cycles, Transfers, and Motivic Homology Theories. (AM-143), Volume 143

By: Vladimir Voevodsky,Andrei Suslin,Eric M. Friedlander

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Cycles, Transfers, and Motivic Homology Theories. (AM-143), Volume 143

By: Vladimir Voevodsky,Andrei Suslin,Eric M. Friedlander

The original goal that ultimately led to this volume was the construction of "motivic cohomology theory," whose existence was conjectured by A. Beilinson and S. Lichtenbaum. This is achieved in the book's fourth paper, using results of the other papers whose additional role is to contribute to our understanding of various properties of algebraic cycles. The material presented provides the foundations for the recent proof of the celebrated "Milnor Conjecture" by Vladimir Voevodsky. The theory of sheaves of relative cycles is developed in the first paper of this volume. The theory of presheaves with transfers and more specifically homotopy invariant presheaves with transfers is the main theme of the second paper. The Friedlander-Lawson moving lemma for families of algebraic cycles appears in the third paper in which a bivariant theory called bivariant cycle cohomology is constructed. The fifth and last paper in the volume gives a proof of the fact that bivariant cycle cohomology groups are canonically isomorphic (in appropriate cases) to Bloch's higher Chow groups, thereby providing a link between the authors' theory and Bloch's original approach to motivic (co-)homology.

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Page Count

261

Publisher

Princeton University Press

Published Date

ISBN 10

140083712X

ISBN 13

9781400837120

Property ($T$) for Groups Graded by Root Systems

By: Mikhail Ershov,Andrei Jaikin-Zapirain,Martin Kassabov

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Property ($T$) for Groups Graded by Root Systems

By: Mikhail Ershov,Andrei Jaikin-Zapirain,Martin Kassabov

The authors introduce and study the class of groups graded by root systems. They prove that if is an irreducible classical root system of rank and is a group graded by , then under certain natural conditions on the grading, the union of the root subgroups is a Kazhdan subset of . As the main application of this theorem the authors prove that for any reduced irreducible classical root system of rank and a finitely generated commutative ring with , the Steinberg group and the elementary Chevalley group have property . They also show that there exists a group with property which maps onto all finite simple groups of Lie type and rank , thereby providing a “unified” proof of expansion in these groups.

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