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arXiv · 2403.00373

Frobenius rigidity in $\mathbb A^1$-homotopy theory

Timo Richarz·Jakob Scholbach
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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 $1$.

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Timo Richarz, Jakob Scholbach. 2024-03-01. Frobenius rigidity in $\mathbb A^1$-homotopy theory. https://arxiv.org/abs/2403.00373

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