Rankin--Eisenstein classes and explicit reciprocity laws
By G. Kings, David Loeffler, Sarah Livia Zerbes. 2015
143 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5231c25be84ad2800a115ef94eeed9f6da430091
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Euler systems for GSp(4) (2017, background): “: H c;d Z p ! Da;b Z p maps the section (e 1;s)c (f 1;s)dover K H;sto the pullback of d [q; 0;q;0] sd a q;b; ;r ]= da;b;q;r, which is true by the construction of the branching maps. Remark 9.3.2. In [KLZ17], the analogous statment for the GL 2 GL 2-moment maps (Lemma 6.3.1) gives rise to a binomial ”
- Iwasawa Main Conjecture for Supersingular Elliptic Curves (2014, background): “Note also that g is cuspidal (which is called “generically non-Eisenstein” in an earlier version) in the sense of [39].”
- Rankin-Eisenstein classes for modular forms (2015, background): “ses of modular forms [Nik11] and certain elliptic curves with complex multiplication [BK11] are known. 1.3. Relation to other works. This paper is the rst in a series, of which the next instalment is [KLZ17]. As it serves as one of the major motivations for the present work, we shall brie y describe”