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Differential coherence of unit-root \(F\)-isocrystals. (Cohérence différentielle des \(F\)-isocristaux unités.) (French. Abridged English version) Zbl 1047.14009
Let \({\mathcal P}\) be a smooth formal scheme over a mixed characteristic complete valuation ring \({\mathcal V}\), \(X\) a smooth subscheme of the special fiber \(P\) of the structural morphism \({\mathcal P}\to{\mathcal V}\), \(T\) a divisor of \(P\) such that \(T_X:=T\cap X\) is a divisor of \(X\), and \({\mathcal D}^+_{\mathcal P}\) the weak completion of the sheaf of differential operators of \({\mathcal P}\). The author proves that the unit-root \(F\)-isocrystals of \(X\setminus T_X\) overconvergent along \(T_X\) are coherent over \({\mathcal D}^+_{{\mathcal P},\mathbb Q}\).

MSC:
14F30 \(p\)-adic cohomology, crystalline cohomology
14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
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