Parabolic restriction conjecture for crystalline monodromy groups

Let f ⁣:VUf\colon V\hookrightarrow U be an open sub-curve, let uV(Fqe)u\in V({\mathbb{F}}_{q^e}) be a base point, and let F{\mathcal{F}} be a convergent FF-isocrystal on UU. Write Gr(fF/V,u)\operatorname{Gr}(f^*{\mathcal{F}}/V,u) and Gr(F/U,u)\operatorname{Gr}({\mathcal{F}}/U,u) for the corresponding monodromy groups. Parabolic restriction conjecture. The subgroup

Gr(fF/V,u)Gr(F/U,u)\operatorname{Gr}(f^*{\mathcal{F}}/V,u)\subset\operatorname{Gr}({\mathcal{F}}/U,u)

is parabolic. No conjectural label or status evidence is included in the supplied span, so the claim may require checking against the surrounding source text.

Sources & referencesView supporting material

Primary source

Urs Hartl and Ambrus Pal, “Crystalline Chebotarëv density theorems”, arXiv:1811.07084 (2025).

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