Geodesic
Frobenius rigidity in $\mathbb{A}^{1}$-homotopy theory
Documenta mathematica, Tome 30 (2025) no. 1, pp. 219-244

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We study the homotopy fixed points under the Frobenius endomorphism on the stable A1-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.
DOI : 10.4171/dm/988
Classification : 14F42, 14G17
Mots-clés : rigidity, K-theory, homotopy theory 
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Timo Richarz; Jakob Scholbach. Frobenius rigidity in $\mathbb{A}^{1}$-homotopy theory. Documenta mathematica, Tome 30 (2025) no. 1, pp. 219-244. doi: 10.4171/dm/988

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