Parabolic restriction conjecture for crystalline monodromy groups

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Let f ⁣:V↪Uf\colon V\hookrightarrow U be an open sub-curve, let u∈V(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⁡(f∗F/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⁡(f∗F/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.

References

Primary source

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

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