Beilinson-flach Elements and Euler Systems Ii: the Birch-swinnerton-dyer Conjecture for Hasse-weil-artin L-series
نویسندگان
چکیده
Let E be an elliptic curve over Q and let be an odd, irreducible twodimensional Artin representation. This article proves the Birch and Swinnerton-Dyer conjecture in analytic rank zero for the Hasse-WeilArtin L-series L(E, , s), namely, the implication L(E, , 1) = 0 ⇒ (E(H)⊗ ) = 0, where H is the finite extension of Q cut out by . The proof relies on padic families of global Galois cohomology classes arising from BeilinsonFlach elements in a tower of products of modular curves.
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