SELMER GROUPS FOR ELLIPTIC CURVES IN Zdl -EXTENSIONS OF FUNCTION FIELDS OF CHAR p
نویسنده
چکیده
Let F be a global field of characteristic p > 0, F/F a Galois extension with Gal(F/F ) ≃ Z l (for some prime l 6= p) and E/F a non-isotrivial elliptic curve. We study the behaviour of Selmer groups SelE(L)r (r any prime) as L varies through the subextensions of F via appropriate versions of Mazur’s Control Theorem. With mild hypotheses on SelE(F )r (essentially a consequence of the Birch and Swinnerton-Dyer conjecture) we prove that SelE(F)r is a cofinitely generated (in some cases cotorsion) Zr[[Gal(F/F )]]-module.
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