article epub_ahead yes Jakub Löwit author e3b80ae2-eb8e-11eb-b029-9aef4a9108a0 GradSch department TaHa department Geometry of the tip of the global nilpotent cone project 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. https://creativecommons.org/licenses/by/4.0/ EMS Press2026 eng equivariant algebraic K-theoryperfection in positive characteristicaffine Grassmannianaffine Schubert varietiesDennis trace mapequivariant Hochschild homologyfixed-point schemestoric varieties 1431-0635 1431-0643 2409.1892510.4171/dm/1064 https://research-explorer.ista.ac.at/record/22694 Löwit, Jakub. “Equivariant K-Theory, Affine Grassmannian and Perfection.” <i>Documenta Mathematica</i>, EMS Press, 2026, doi:<a href="https://doi.org/10.4171/dm/1064">10.4171/dm/1064</a>. J. Löwit, Documenta Mathematica (2026). Löwit, J. (2026). Equivariant K-theory, affine Grassmannian and perfection. <i>Documenta Mathematica</i>. EMS Press. <a href="https://doi.org/10.4171/dm/1064">https://doi.org/10.4171/dm/1064</a> Löwit, Jakub. “Equivariant K-Theory, Affine Grassmannian and Perfection.” <i>Documenta Mathematica</i>. EMS Press, 2026. <a href="https://doi.org/10.4171/dm/1064">https://doi.org/10.4171/dm/1064</a>. Löwit J. Equivariant K-theory, affine Grassmannian and perfection. <i>Documenta Mathematica</i>. 2026. doi:<a href="https://doi.org/10.4171/dm/1064">10.4171/dm/1064</a> J. Löwit, “Equivariant K-theory, affine Grassmannian and perfection,” <i>Documenta Mathematica</i>. EMS Press, 2026. Löwit J. 2026. Equivariant K-theory, affine Grassmannian and perfection. Documenta Mathematica. 226932026-08-12T13:29:17Z2026-08-13T07:00:17Z