Automorphisms of Frobenius twisted de Rham cohomology
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914055593132032 |
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| author | Li, Shizhang Mondal, Shubhodip |
| author_facet | Li, Shizhang Mondal, Shubhodip |
| contents | In this short paper, we prove that the moduli of automorphisms of Frobenius twisted de Rham cohomology functor is given by $\mathbb{G}_m$. Our method is to use the notion of $\mathbb{G}_a^{\mathrm{perf}}$-modules and its connection to the de Rham cohomology functor introduced in \cite{M22}. As an application of the induced $\mathbb{G}_m$-action, we reprove a result of Bhatt, Petrov, and Vologodsky on the decomposition of the Frobenius twisted de Rham complex. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_17279 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Automorphisms of Frobenius twisted de Rham cohomology Li, Shizhang Mondal, Shubhodip Algebraic Geometry Algebraic Topology 14F30, 14F40 In this short paper, we prove that the moduli of automorphisms of Frobenius twisted de Rham cohomology functor is given by $\mathbb{G}_m$. Our method is to use the notion of $\mathbb{G}_a^{\mathrm{perf}}$-modules and its connection to the de Rham cohomology functor introduced in \cite{M22}. As an application of the induced $\mathbb{G}_m$-action, we reprove a result of Bhatt, Petrov, and Vologodsky on the decomposition of the Frobenius twisted de Rham complex. |
| title | Automorphisms of Frobenius twisted de Rham cohomology |
| topic | Algebraic Geometry Algebraic Topology 14F30, 14F40 |
| url | https://arxiv.org/abs/2509.17279 |