Vol. 2, No. 2, 2017

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

Amalendu Krishna and Charanya Ravi

Vol. 2 (2017), No. 2, 235–275
Abstract

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