Equivariant vector bundles, their derived category and K-theory on affine schemes

Let $G$ be an affine group scheme over a noetherian commutative ring $R$ . We show that every $G$ -equivariant vector bundle on an affine toric scheme over $R$ with $G$ -action is equivariantly extended from $Spec (R)$ for several cases of $R$ and $G$ .

We show that, given two affine schemes with group scheme actions, an equivalence of the equivariant derived categories implies isomorphism of the equivariant $K$ -theories as well as equivariant $K^{'}$ -theories.

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Keywords

group scheme action, equivariant vector bundles, equivariant $K$-theory

Mathematical Subject Classification 2010

Primary: 13C10

Secondary: 14L30

Milestones

Received: 30 September 2015

Revised: 10 May 2016

Accepted: 30 May 2016

Published: 14 December 2016

Authors

Amalendu Krishna
School of Mathematics Tata Institute of Fundamental Research 1 Homi Bhabha Road Colaba Mumbai 400005 India

Charanya Ravi
School of Mathematics Tata Institute of Fundamental Research 1 Homi Bhabha Road Colaba Mumbai 400005 India

Vol. 2, No. 2, 2017

Amalendu Krishna and Charanya Ravi

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors