TORSION p-ADIC GALOIS REPRESENTATIONS
نویسنده
چکیده
Let p be a prime, K a finite extension of Qp and T a finite free Zp-representation of Gal(K̄/K). We prove that T ⊗Zp Qp is semi-stable (resp., crystalline) with Hodge-Tate weights in {0, . . . , r} if and only if for all n, T/pnT is torsion semi-stable (resp., crystalline) with Hodge-Tate weights in {0, . . . , r}. Résumé. (Représentations galoisiennnes p-adiques de torsion) Soient p un nombre premier, r un entier positif, K une extension finie de Qp et T une Zp-représentation de Gal(K̄/K) libre de rang fini en tant que Zp-module. On montre que T ⊗Zp Qp est semi-stable (resp. cristalline) á poids de Hodge-Tate dans {0, . . . , r} si, et seulement si pour tout entier n, la représentation T/pnT est le quotient de deux réseaux dans une représentation semi-stable (resp. cristalline) poids de Hodge-Tate dans {0, . . . , r}.
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