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On the Cartan map for crossed products and Hopf-Galois extensions

Konstantin Ardakov·Simon Wadsley
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Abstract

We study certain aspects of the algebraic K-theory of Hopf-Galois extensions. We show that the Cartan map from K-theory to G-theory of such an extension is a rational isomorphism, provided the ring of coinvariants is regular, the Hopf algebra is finite dimensional and its Cartan map is injective in degree zero. This covers the case of a crossed product of a regular ring with a finite group and has an application to the study of Iwasawa modules.

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BibTeXRIS

Konstantin Ardakov, Simon Wadsley. 2007-03-22. On the Cartan map for crossed products and Hopf-Galois extensions. https://arxiv.org/abs/math/0703664

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