Applications of Algebraic K-Theory to Algebraic Geometry and Number Theory.

Format:

Book

Author/Creator:

Bloch, Spencer.

Contributor:

Dennis, R. Keith.

Friedlander, Eric M.

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132

Contemporary mathematics, 55 0271-4132

Language:

English

Subjects (All):

Algebraic number theory--Congresses.

Geometry, Algebraic--Congresses.

K-theory--Congresses.

Local Subjects:

Algebraic number theory--Congresses.

Geometry, Algebraic--Congresses.

K-theory--Congresses.

Physical Description:

1 online resource (432 p.)

Edition:

1st ed.

Place of Publication:

Providence : American Mathematical Society, 1986.

Language Note:

English

Summary:

This volume presents a state-of-the-art description of some of the exciting applications of algebraic $K$-theory to other branches of mathematics, especially algebraic geometry and algebraic number theory. As the proceedings of a 1983 AMS-IMS-SIAM Joint Summer Research Conference, it includes current and important work by some of the best researchers in the field. The diverse scope includes the following topics: the matrix/vector bundle tradition of concrete computations for specific rings, the interaction with algebraic cycles, and the generalization of the regulator map for units in an algebraic number field to higher $K$-groups of varieties over number fields. Of particularly high research value are the ideas of Beilinsonon, which are presented here for the first time, the work of Merkurjev and Suslin relating $K$-theory to the Brauer group (as reported by Merkurjev and Wadsworth), and the papers by Kato on algebraic cycles. Directed towards mathematicians working in algebraic $K$-theory, algebraic geometry, and algebraic number theory, this volume is also of interest to the algebraic topologist. The reader should be familiar with basic $K$-theory and interested in its applications to other areas of mathematics.

Contents:

The homotopy type of FÏ?q. The complex and symplectic cases

On the 2-primary part of the Birch-Tate conjecture for cyclotomic fields

K2 of fields and the Brauer group

Torsion in homotopy equivalences of S1-bundles

Properties of the wild kernel of K2 of global fields

Central extensions of SL2 over division rings and some metaplectic theorems

Constructing algebraic K-theory elements from K1A

The equivariant second Stiefel-Whitney class, the characteristic classes of symmetric bilinear forms and orthogonal Galois representations.

Notes:

Description based upon print version of record.

Includes bibliographies.

Description based on print version record.

ISBN:

0-8218-7642-2