Projective p-adic representations of the K-rational geometric fundamental group
Identifieur interne : 001231 ( Main/Merge ); précédent : 001230; suivant : 001232Projective p-adic representations of the K-rational geometric fundamental group
Auteurs : G. Frey [États-Unis] ; E. Kani [États-Unis]Source :
- Archiv der Mathematik [ 0003-889X ] ; 2001-07-01.
Abstract
Abstract.: If C/K is a curve over a finitely generated field K with a K-rational point $P \in C(K)$ , then the K-rational geometric fundamental group of C/K is the Galois group $\pi_1(C,P)=\rm{Gal}(F_{nr,P}/F)$ of the maximal unramified extension F nr,P of $F=\kappa(C)$ in which P splits completely.¶In view of the Fontaine-Mazur Conjecture, it is of interest to know examples of curves for which this group is infinite, and this is implied by the existence of projective p-adic representations $\tilde{\rho}_V:\pi_1(C,P)\rightarrow {\rm PGL}(V)$ with infinite image.¶In this paper we first derive some necessary and sufficient conditions that the projective Galois representation $\tilde{\rho}_V:G_F\rightarrow {\rm PGL}(V)$ attached to a p-adic submodule $V\subset T_p(A)$ of the Tate-module of an abelian variety A/F factors over $\pi_1(C,P)$ . We then apply this (in positive characteristic) to present two constructions for such representations: one by properties of moduli spaces and the other by cyclic coverings.
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DOI: 10.1007/PL00000463
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