PreprintOvercoherence : holonomicity of unitroot FisocrystalsDaniel CaroAbstractLet \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 unitroot Fisocrystals 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: padique cohomology, arithmetic Dmodules, holonomicity, Fisocrystals. AMS Subject Classification: Primary 14F30.
