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Bi-relative algebraic K-theory and topological cyclic homology | | Thomas Geisser
; Lars Hesselholt
; | | Date: |
8 Sep 2004 | | Subject: | Number Theory; K-Theory and Homology | math.NT math.KT | | Abstract: | It is well-known that algebraic K-theory preserves products of rings. However, in general, algebraic K-theory does not preserve fiber-products of rings, and bi-relative algebraic K-theory measures the deviation. It was proved by Cortinas that,rationally, bi-relative algebraic K-theory and bi-relative cyclic homology agree. In this paper, we show that, with finite coefficients, bi-relative algebraic K-theory and bi-relative topological cyclic homology agree. As an application, we show that for a, possibly singular, curve over a perfect field of positive characteristic p, the cyclotomic trace map induces an isomorphism of the p-adic algebraic K-groups and the p-adic topological cyclic homology groups in non-negative degrees. As a further application, we show that the difference between the p-adic K-groups of the integral group ring of a finite group and the p-adic K-groups of a maximal Z-order in the rational group algebra can be expressed entirely in terms of topological cyclic homology. | | Source: | arXiv, math.NT/0409122 | | Services: | Forum | Review | PDF | Favorites | |
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