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- W2023982694 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 $tilde{rho}_V:G_Frightarrow {rm PGL}(V)$ attached to a p-adic submodule $Vsubset T_p(A)$ 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." @default.
- W2023982694 created "2016-06-24" @default.
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- W2023982694 date "2001-07-01" @default.
- W2023982694 modified "2023-10-04" @default.
- W2023982694 title "Projective p-adic representations of the K-rational geometric fundamental group" @default.
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- W2023982694 doi "https://doi.org/10.1007/pl00000463" @default.
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