References & Citations
Mathematics > Algebraic Geometry
Title: Frobenius rigidity in $\mathbb A^1$-homotopy theory
(Submitted on 1 Mar 2024 (v1), last revised 5 Apr 2024 (this version, v2))
Abstract: We study the homotopy fixed points under the Frobenius endomorphism on the stable $\mathbb A^1$-homotopy category of schemes in characteristic $p>0$ and prove a rigidity result for cellular objects in these categories after inverting $p$. As a consequence we determine the analogous fixed points on the $K$-theory of algebraically closed fields in positive characteristic. We also prove a rigidity result for the homotopy fixed points of the partial Frobenius pullback on motivic cohomology groups in weights at most $1$.
Submission history
From: Timo Richarz [view email][v1] Fri, 1 Mar 2024 08:57:30 GMT (38kb)
[v2] Fri, 5 Apr 2024 13:21:41 GMT (37kb)
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