Curves with infinite K-rational geometric fundamental group
نویسندگان
چکیده
where Πg(C) is the geometric (profinite) fundamental group of C×Spec(Ks) (i.e. Πg(C) is equal to the Galois group of the maximal unramified extension of F (C)⊗Ks). This sequence induces a homomorphism ρC from GK to Out(Πg(C)) which is the group of automorphisms modulo inner automorphisms of Πg(C). It is well known that ρC is an important tool for studying C. For instance, it determines C up to K−isomorphisms if the genus of C is at least 2 and K is a number field or even a p−adic field (see [Mo]).
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