Resumen de Constructible ∇∇-modules on curves

Bernard Le Stum

• Let V be a complete discrete valuation ring of mixed characteristic with perfect residue field. Let X be a geometrically connected smooth proper curve over V.

  We introduce the notion of constructible convergent ∇-module on the analytification Xan K of the generic fiber of X. A constructible module is an OXan K -module which is not necessarily coherent, but becomes coherent on a stratification by locally closed subsets of the special fiber Xk of X. The notions of connection, of (over-) convergence and of Frobenius structure carry over to this situation. We describe a specialization functor from the category of constructible convergent ∇-modules to the category of D† Xˆ Qmodules.

  We show that specialization induces an equivalence between constructible F-∇-modules and perverse holonomic F-D† Xˆ Q -modules.