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 SS, giving rise on the spectrum of a field S=\SpeckS=\Spec\,k to local symbols of class field theory. Relative local symbols are obtained in terms of the universal property of a couple (,f)(\Im,f), of a SS-group functor \Im, associated to a SS-formal curve X{ \char 88} locally of the form { \char 88}={\text Spf}\, A&quaa;&quaa;T&quac;&quac; (S=\SpecA)S=\Spec\,A). \Im is a SS-group extension of the completion Wˇ\check{W} of the universal SS-Witt vectors group WW, by the group of units {\cal O}_{S}&quaa;&quaa;T&quac;&quac;^{*}. We associate an SS-functor omb\Im_{\text omb} to \Im, 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