Gersten conjecture for equivariant K-theory and applications

Krishna, Amalendu (2010) Gersten conjecture for equivariant K-theory and applications Mathematische Annalen, 347 (1). pp. 123-133. ISSN 0025-5831

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For a reductive group scheme G over a regular semi-local ring A, we prove the Gersten conjecture for the equivariant K-theory. As a consequence, we show that if F is the field of fractions of A, then KG0(A)≅KG0(F), generalizing the analogous result for a dvr by Serre (Inst Hautes Études Sci Publ Math 34:37-52, 1968). We also show the rigidity for the K-theory with finite coefficients of a Henselian local ring in the equivariant setting. We use this rigidity theorem to compute the equivariant K-theory of algebraically closed fields.

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