## Oberwolfach Reports

Algebraic studies of the Whitehead group began in the s. A related field is the study of the structure of linear groups over arbitrary rings, in particular, the theory of determinants over a skew-field [Ar]. Grothendieck in Moreover, the previously familiar representation rings, Witt rings cf.

- “Classical” Algebraic K-Theory, and Connections with Arithmetic;
- “Classical” algebraic K-theory and connections with arithmetic?
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- Algebro-Geometric and Homotopical Methods.

Witt ring of classes of quadratic forms, etc. It became clear, moreover, that this construction reveals new perspectives in the understanding of old analytical problems the index problem of elliptic operators , topological problems extraordinary homology theories , and the theory of group representations.

Congruence subgroup and an algebraic analogue of the Bott periodicity theorem — the theory of polynomial extensions — was obtained. Spectrum of a ring. In algebraic geometry there are important connections with the Chow groups cf. Chow ring.

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## Representation Theory and Higher Algebraic K-Theory - CRC Press Book

Algebro-Geometric and Homotopical Methods 16 January - 30 April One pillar of our subject is the foundational work of Alexander Grothendieck, especially his introduction of K-theory in his proof of the generalized Riemann-Roch Theorem. Eric M. Lars Hesselholt. Authors Authors and affiliations A. This process is experimental and the keywords may be updated as the learning algorithm improves. This is a preview of subscription content, log in to check access.

Beilinson A. Google Scholar. Soviet Math. MathSciNet Google Scholar. Bloch S. Notes, U.

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Irvine, Dupont J. Pure and Appl. Algebra, 44 , — Algebra, 25 , p. Characteristic classes of flat bundles, Preprint Gabrielov A. Analysis and its Applications, 9 2 , , p.

### 1st Edition

Gelfand I. Goncharov A. To appear in Advances in Mathematics.