The generalized Cassels-Tate dual exact sequence for 1-motives
نویسندگان
چکیده
منابع مشابه
The Yoga of the Cassels-tate Pairing
Cassels has described a pairing on the 2-Selmer group of an elliptic curve which shares some properties with the Cassels-Tate pairing. In this article, we prove that the two pairings are the same.
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〈·, ·〉A : X(A)×X(A∨)→ Q/Z such that X(A)div annhilates X(A∨) and vice-versa with the roles of A and A∨ swapped, and the induced pairing X(A)nd ×X(A)nd → Q/Z will be perfect in the sense that the annihilator of each side of the pairing vanishes in the other side. (It is known that for each prime `, the `-primary part of X(A)nd is finite.) Moreover, for any symmetric isogeny φ : A→ A∨ (e.g. a pol...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2009
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2009.v16.n5.a6