Beilinson-Flach elements and Euler systems II: The Birch-Swinnerton-Dyer conjecture for Hasse-Weil-Artin $L$-series
نویسندگان
چکیده
منابع مشابه
Beilinson-flach Elements and Euler Systems Ii: the Birch-swinnerton-dyer Conjecture for Hasse-weil-artin L-series
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 c...
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This article establishes new cases of the Birch and Swinnerton-Dyer conjecture in analytic rank 0, for elliptic curves over Q viewed over the fields cut out by certain self-dual Artin representations of dimension at most 4. When the associated L-function vanishes (to even order ≥ 2) at its central point, two canonical classes in the corresponding Selmer group are constructed and shown to be lin...
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We give a brief description of the Birch-Swinnerton-Dyer conjecture which is one of the seven Clay problems.
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A polynomial relation f(x, y) = 0 in two variables defines a curve C. If the coefficients of the polynomial are rational numbers then one can ask for solutions of the equation f(x, y) = 0 with x, y ∈ Q, in other words for rational points on the curve. If we consider a non-singular projective model C of the curve then over C it is classified by its genus. Mordell conjectured, and in 1983 Falting...
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This essay starts by first explaining, for elliptic curves defined over Q, the statement of the conjecture of Birch and Swinnerton-Dyer. Alongside, it contains a discussion of some results that have been proved in the direction of the conjecture, such as the theorem of Kolyvagin-Gross-Zagier and the weak parity theorem of Tim and Vladimir Dokchitser. The second, third and fourth part of the ess...
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ژورنال
عنوان ژورنال: Journal of Algebraic Geometry
سال: 2015
ISSN: 1056-3911,1534-7486
DOI: 10.1090/s1056-3911-2015-00675-0