On the Euler-Poincaré characteristics of finite dimensional $p$-adic representations..

J. Coates , R. Sujatha , Jean-Pierre Wintenberger (1)

1 IRMA - Institut de Recherche Mathématique Avancée

Using the theory of $p$-adic Galois-representations of local fields of J.-M. Fontaine, we prove some vanishing results for the cohomology of the image of Galois in $p$-adic representations associated to motives over local and number fields. We deduce from these results the calculation of the Euler-characteristics of these representations under suitable hypotheses.

Mots clés: Galois representations

Domaines: Théorie des nombres [math.NT]

J. Coates, R. Sujatha, Jean-Pierre Wintenberger. On the Euler-Poincaré characteristics of finite dimensional $p$-adic representations... Publications mathematiques de l' IHES, 2001, 93, pp.107-143. ⟨10.1007/s10240-001-8189-x⟩. ⟨hal-00129640⟩