Euler systems for Rankin–Selberg convolutions of modular forms
By Antonio Lei, David Loeffler, Sarah Livia Zerbes. 2012
123 citations recorded by the source corpus.
We construct a Euler system in the cohomology of the tensor product of the Galois representations attached to two modular forms, using elements in the higher Chow groups of products of modular curves. We use these elements to prove a finiteness theorem for the strict Selmer group of the Galois representation when the associated p-adic Rankin–Selberg L-function is nonvanishing at s=1.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/32eaae519292912591ece58e251b5b57fb5b0605
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Rankin--Eisenstein classes and explicit reciprocity laws (2015, methodology): “(The projection to the ordinary part is required in order to obtain analytic variation in the cyclotomic variable j, an observation which also goes back to [24].”
- Euler systems for GSp(4) (2017, methodology): “ore at all other primes. Remark 8.4.2. These alternative local choices will give elements related to the \non-dashed" versions in the same way as the elements Z ::: relate to the elements ::: in [LLZ14]. As in op.cit., it is the nondashed versions which are of interest for applications, but the”