We construct a generalization of the field of norms functor, due to J.-M. Fontaine and J.-P. Wintenberger for local fields, in the case of a ring R which is p-adically formally étale over the Tate algebra of convergent power series over a complete discrete valuation ring V of characteristic 0 and with perfect residue field of positive characteristic p. We use this to show that the category of p-adic representations of the fundamental group of is equivalent, as a tensor abelian category, to the category of so-called étale (φ,ΓR)-modules.
Generalized ring of norms and generalized $(varphi,Gamma)$--modules / F. Andreatta. - In: ANNALES SCIENTIFIQUES DE L'ECOLE NORMALE SUPERIEURE. - ISSN 0012-9593. - 39:4(2006), pp. 599-647. [10.1016/j.ansens.2006.07.003]
Generalized ring of norms and generalized $(varphi,Gamma)$--modules
F. AndreattaPrimo
2006
Abstract
We construct a generalization of the field of norms functor, due to J.-M. Fontaine and J.-P. Wintenberger for local fields, in the case of a ring R which is p-adically formally étale over the Tate algebra of convergent power series over a complete discrete valuation ring V of characteristic 0 and with perfect residue field of positive characteristic p. We use this to show that the category of p-adic representations of the fundamental group of is equivalent, as a tensor abelian category, to the category of so-called étale (φ,ΓR)-modules.Pubblicazioni consigliate
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