Overcoherence : holonomicity of unit-root F-isocrystals

Daniel Caro

Abstract

Let \V be a mixed characteristic complete discrete valuation ring, \PP a smooth formal scheme over \V, P its special fiber, X a smooth subscheme of P, T a divisor in P such that T _X = T ∩ X is a divisor in X. We prove that the unit-root F-isocrystals on X – T _X overconvergent along T _X are holonomic. Furthermore, we show that the stability of the holonomicity by extraordinary inverse image imply the stability of the holonomicity by the directe image of a proper morphism.

Keywords: p-adique cohomology, arithmetic D-modules, holonomicity, F-isocrystals.

AMS Subject Classification: Primary 14F30.