Constructible ∇∇-modules on curves

• Bernard Le Stum ^[1]
  1. [1] Université de Rennes 1
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 20, Nº. 2, 2014, págs. 627-674
• Idioma: inglés
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• Resumen

  • 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.