The curve restriction conjecture for irreducible overconvergent F-isocrystals

Let XX be a variety, let FIsoc(X)\operatorname{\mathbf{F-Isoc}}^\dagger(X) denote the category of overconvergent FF-isocrystals on XX, and let CXC \subseteq X be a curve. Curve restriction conjecture. For every irreducible EFIsoc(X)\mathcal{E} \in \operatorname{\mathbf{F-Isoc}}^\dagger(X), there exists a curve CXC \subseteq X such that the pullback of E\mathcal{E} to FIsoc(C)\operatorname{\mathbf{F-Isoc}}^\dagger(C) is irreducible. This is expected by analogy with Wiesend's theorem in the \ell-adic setting, but the source gives an approach only when the base field is finite.

Sources & referencesView supporting material

Primary source

Kiran S. Kedlaya, “Notes on isocrystals”, arXiv:1606.01321 (2022).

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