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arXiv · 2409.18925

Equivariant $K$-theory, affine Grassmannian and perfection

Jakub Löwit
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Abstract

We study torus-equivariant algebraic $K$-theory of affine Schubert varieties in the perfect affine Grassmannians over $\mathbb{F}_p$. 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 $\mathbb{F}_p$-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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Jakub Löwit. 2024-09-27. Equivariant $K$-theory, affine Grassmannian and perfection. https://doi.org/10.4171/dm%2F1064

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