Kings, G;
Loeffler, D;
Zerbes, SL;
(2017)
Rankin–Eisenstein classes and explicit reciprocity laws.
Cambridge Journal of Mathematics
, 5
(1)
pp. 1-122.
10.4310/CJM.2017.v5.n1.a1.
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Abstract
We construct three-variable p-adic families of Galois cohomology classes attached to Rankin convolutions of modular forms, and prove an explicit reciprocity law relating these classes to critical values of L-functions. As a consequence, we prove finiteness results for the Selmer group of an elliptic curve twisted by a 2-dimensional odd irreducible Artin representation when the associated L-value does not vanish.
| Type: | Article |
|---|---|
| Title: | Rankin–Eisenstein classes and explicit reciprocity laws |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4310/CJM.2017.v5.n1.a1 |
| Publisher version: | http://dx.doi.org/10.4310/CJM.2017.v5.n1.a1 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1497960 |
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