Beilinson-Flach elements and Euler systems I: syntomic regulators and p-adic Rankin L-series
By M. Bertolini, Henri Darmon, Victor Rotger. 2014
53 citations recorded by the source corpus.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/86602cd272de74143d496e3f015b8825feee1a24
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Euler systems for Rankin–Selberg convolutions of modular forms (2012, methodology): “If in fact χ is primitive modulo N , then both sides are zero unless α has exact order N , so we may reduce to precisely the case covered by [BDR12].”
- Rankin--Eisenstein classes and explicit reciprocity laws (2015, methodology): “–Eisenstein class in Besser’s p-adic rigid syntomic cohomology (a cohomology theory built up from p-adic rigid-analytic differential forms), for a prime p∤N, extending the case k= k′ = j= 0 treated in [BDR15a]. There, in a completely parallel way, we find that pairing this syntomic Rankin–Eisenstein c”
- Rankin-Eisenstein classes for modular forms (2015, methodology): “on 4.2.1] and the formulae in (3.5.1) with r= k+ 2, r0= k0+ 2. 6.3. Finite-polynomial cohomology. We now compute the image of the Eisenstein class under the p-adic syntomic Abel{Jacobi map, following [BDR15a] and [DR14]. In order that we can apply Besser’s rigid syntomic cohomology, we need to assum”
- Rankin–Eisenstein classes in Coleman families (2015, methodology): “We also proved an “explicit reciprocity law” relating certain specialisations of these families to critical values of Rankin–Selberg L-functions, with applications to the Birch–Swinnerton-Dyer conjecture for Artin twists of p-ordinary elliptic curves, extending earlier works of Bertolini– Darmon–Rot”
- Euler systems for modular forms over imaginary quadratic fields (2013, background): “4 of [LLZ14], which is a very slight variation on the main theorem of [BDR12], now gives the following:”