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The exposition includes, besides K-theory, a considerable amount of related arithmetic. User Account Log in Register Help. Search Close Advanced Search Help.

ChroK - Chromatic homotopy and K-theory

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Algebraic K-Theory and Its Geometric Applications

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. 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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Algebraic geometric codes and their applications - Gil Cohen

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Contemporary Math., vol. 55

References [Ar] E. Atiyah, "K-theory. Bass, "Lectures on topics in algebraic K-theory", Tata Inst. Manin, "Lectures on the K-functor in algebraic geometry" Russian Math.