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For certain tame abelian covers of arithmetic surfaces we obtain formulas, involving a quadratic form derived from intersection numbers, for the equivariant Euler characteristics of both the canonical sheaf and also its square root. These formulas allow us to carry out explicit calculations; in particular, we are able to exhibit examples where these two Euler characteristics and that of the structure sheaf are all different and non-trivial. Our results are obtained by using resolvent techniques...
Nous étudions la structure de certains espaces homogènes principaux associés aux éléments du groupe de Selmer d’une courbe elliptique à multiplication complexe. Nous utilisons des résultats de Rubin pour construire, à partir des unités elliptiques, des espaces homogènes principaux de structure galoisienne non triviale. Cette construction fournit un lien nouveau entre un problème de structure galoisienne et certaines fonctions -adiques.
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