Frobenius rigidity in $\mathbb A^1$-homotopy theory
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910398932844544 |
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| author | Richarz, Timo Scholbach, Jakob |
| author_facet | Richarz, Timo Scholbach, Jakob |
| contents | 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 $1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00373 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Frobenius rigidity in $\mathbb A^1$-homotopy theory Richarz, Timo Scholbach, Jakob Algebraic Geometry 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 $1$. |
| title | Frobenius rigidity in $\mathbb A^1$-homotopy theory |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2403.00373 |