Integral Eisenstein cocycles on GLn , I: Sczech's cocycle and p-adic L-functions of Totally Real Fields - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Cambridge Journal of Mathematics Année : 2014

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.
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Dates et versions

hal-02981532 , version 1 (28-10-2020)

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  • HAL Id : hal-02981532 , version 1

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Pierre Charollois, Samit Dasgupta. Integral Eisenstein cocycles on GLn , I: Sczech's cocycle and p-adic L-functions of Totally Real Fields. Cambridge Journal of Mathematics, 2014. ⟨hal-02981532⟩
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