Integral Eisenstein cocycles on GLn , I: Sczech's cocycle and p-adic L-functions of Totally Real Fields
Résumé
We define an integral version of Sczech's Eisenstein cocycle on GLn by smoothing at a prime. As a result we obtain a new proof of the integrality of the values at nonpositive integers of the smoothed partial zeta functions associated to ray class extensions of totally real fields. We also obtain a new construction of the p-adic L-functions associated to these extensions. Our cohomological construction allows for a study of the leading term of these p-adic L-functions at s = 0. We apply Spiess's formalism to prove that the order of vanishing at s = 0 is at least equal to the expected one, as conjectured by Gross. This result was already known from Wiles' proof of the Iwasawa Main Conjecture.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)
Loading...