Kedlaya's minimal slope conjecture for overconvergent F-isocrystals
Kedlaya's minimal slope conjecture for overconvergent F-isocrystals
Let be a smooth connected scheme separated of finite type over . Let and be irreducible overconvergent -isocrystals on , and let and be the associated convergent -isocrystals. Suppose they admit slope filtrations and , respectively. An isomorphism is an isomorphism between their minimal-slope constituents. Kedlaya's minimal slope conjecture. If such an isomorphism exists, then there is a unique isomorphism of overconvergent -isocrystals such that the induced diagram from and the associated isomorphism commutes in the category of convergent -isocrystals on . The conjecture concerns whether the overconvergent objects are determined by the minimal-slope constituent of their slope filtrations. It is trivially true when is proper; over a finite field, Ambrosi and D'Addezio proved a rank-one case under a nontriviality hypothesis on , while the stronger version without that hypothesis remains under study.
Sources & referencesView supporting material
Primary source
Nobuo Tsuzuki, “Minimal slope conjecture of F-isocrystals”, arXiv:1910.03871 (2021).
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