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- W4386869537 abstract "Rigid connections over a variety $$X_{{mathbb C}}$$ smooth projective over $${mathbb C}$$ , while restricted to the formal p-completion $$hat X_W$$ of a non-ramified projective p-adic model $$X_W$$ of $$X_{mathbb C}$$ , yield F-isocrystals. This is proved in Esnault and Groechenig (Acta Math 225(1):103–158, 2020, Theorem 1.6), using the theory of Higgs-de Rham flows on the mod p reduction of $$X_W$$ . We give here a p-adic proof of this theorem, obtained with Johan de Jong, which relies on the fact that for $$pge 3$$ , the Frobenius pull-back of a connection on $$hat X_W$$ is well defined, whether the p-curvature of the mod p reduction is nilpotent or not. However this proof so far does not give the crystallinity property proved in Esnault and Groechenig (Acta Math 225(1):103–158, 2020, Theorem 5.4) which can be expressed by saying that the p-adic local systems obtained on the p-adic variety $$X_{overline {mathrm {Frac}(W)}}$$ for p large descend to a crystalline local system over $$X_{mathrm {Frac}(W)}$$ . The version under the strong cohomological rigidity of the same theorem is worked out in Esnault and Groechenig (Frobenius structures and unipotent monodromy at infinity, Preprint 2021, 8 pp.). We defer this discussion to Chap. 9 ." @default.
- W4386869537 created "2023-09-20" @default.
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- W4386869537 date "2023-01-01" @default.
- W4386869537 modified "2023-09-27" @default.
- W4386869537 title "Lecture 8: Rigid Local Systems and F-Isocrystals" @default.
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- W4386869537 doi "https://doi.org/10.1007/978-3-031-40840-3_8" @default.
- W4386869537 hasPublicationYear "2023" @default.
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