Equivariant K-theory, affine Grassmannian and perfection
Löwit J. 2026. Equivariant K-theory, affine Grassmannian and perfection. Documenta Mathematica.
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Abstract
We study torus-equivariant algebraic K-theory of affine Schubert varieties in the perfect affine Grassmannians over Fp. 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 Fp-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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2026-03-26
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Documenta Mathematica
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EMS Press
Acknowledgement
I would like to thank the following people for fruitful discussions,
helpful sanity checks or comments on previous drafts: Roman Bezrukavnikov, Jens Niklas Eberhardt, Mischa Elkner, Tamás Hausel, Andres Fernandez Herrero, Adeel Khan,
Bernhard Köck, Andrei Konovalov, Quoc Ho, Mirko Mauri, Matthew Morrow, Charanya
Ravi, Kamil Rychlewicz, Shyiu Shen, Vladimir Sosnilo, Georg Tamme, Xinwen Zhu. I
would further like to thank Marc Hoyois and the anonymous referee for spotting an error
in a previous version.
This work was done during author’s PhD at the Institute of Science and Technology Austria (ISTA). It was funded by a DOC Fellowship of the Austrian Academy
of Sciences and by the Austrian Science Fund (FWF) 10.55776/P35847. For open access
purposes, the author has applied a CC BY public copyright license to any author-accepted
manuscript version arising from this submission.
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Cite this
Löwit J. Equivariant K-theory, affine Grassmannian and perfection. Documenta Mathematica. 2026. doi:10.4171/dm/1064
Löwit, J. (2026). Equivariant K-theory, affine Grassmannian and perfection. Documenta Mathematica. EMS Press. https://doi.org/10.4171/dm/1064
Löwit, Jakub. “Equivariant K-Theory, Affine Grassmannian and Perfection.” Documenta Mathematica. EMS Press, 2026. https://doi.org/10.4171/dm/1064.
J. Löwit, “Equivariant K-theory, affine Grassmannian and perfection,” Documenta Mathematica. EMS Press, 2026.
Löwit J. 2026. Equivariant K-theory, affine Grassmannian and perfection. Documenta Mathematica.
Löwit, Jakub. “Equivariant K-Theory, Affine Grassmannian and Perfection.” Documenta Mathematica, EMS Press, 2026, doi:10.4171/dm/1064.
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