Equivariant K-theory, affine Grassmannian and perfection

2024/09/27 by Löwit, Jakub · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2409.18925

Abstract

We study torus-equivariant algebraic K-theory of affine Schubert varieties in the perfect affine Grassmannians over \mathbbF_p. We further compare it to the torus-equivariant Hochschild homology of perfect complexes, which has a geometric description in terms of global functions on certain fixed-point schemes. We prove that \mathbbF_p-linearly, this comparison is an isomorphism. Our approach is quite constructive, resulting in new computations of these K-theory rings. We establish various structural results for equivariant perfect algebraic K-theory on the way; we believe these are of independent interest.

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