Jacobienne locale d'une courbe formelle relative

  • Carlos Contou-Carrère

    Université de Montpellier II, France


This article is devoted to the proof of a relative duality formula on a noetherian scheme , giving rise on the spectrum of a field \( S=\Spec\,k \) to local symbols of class field theory. Relative local symbols are obtained in terms of the universal property of a couple , of a -group functor , associated to a -formal curve locally of the form \( { \char 88}={\text Spf}\, A&quaa;&quaa;T&quac;&quac; \) (\( S=\Spec\,A) \). is a -group extension of the completion of the universal -Witt vectors group , by the group of units \( {\cal O}_{S}&quaa;&quaa;T&quac;&quac;^{*} \). We associate an -functor to , and we define an Abel-Jacobi morphism \( f:{ \char 85}=\Spec\ A&quaa;&quaa;T&quac;&quac;&quaa;T^{-1}&quac;\,\longrightarrow \,\Im_{\text omb} \) , setting up a group isomorphism:

Cite this article

Carlos Contou-Carrère, Jacobienne locale d'une courbe formelle relative. Rend. Sem. Mat. Univ. Padova 130 (2013), pp. 1–106

DOI 10.4171/RSMUP/130-1