ℓ-adic Representations Associated to Modular Forms over Imaginary Quadratic Fields
By Tobias Berger, Gergely Harcos. 2007
61 citations recorded by the source corpus.
Let p be a regular algebraic cuspidal automorphic representation of GL(2) over an imaginary quadratic number field K, and let l be a prime number. Assuming the central character of p is invariant under the nontrivial automorphism of K, it is shown that there is a continuous irreducible l-adic representation rho of Gal((K) over bar /K) such that L(s, rho(v)) = L(s, pi(v)) whenever v is a prime of K outside an explicit finite set.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/54d9248342e05148769e6dfbab0cd3403282521c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Discrete Mathematics and Combinatorics
In Geometry and Topology
- Akshay Venkatesh
- Frank Calegari
- A. Brumer
- Barry Mazur
- Ken Kramer
- Nicolas Bergeron
- P. Michel
- R. Munshi
In Mathematical Physics
- Akshay Venkatesh
- Frank Calegari
- A. Brumer
- Barry Mazur
- Ken Kramer
- Nicolas Bergeron
- P. Michel
- R. Munshi
Citations in the corpus
- A torsion Jacquet--Langlands correspondence (2012, methodology): “Since we have a characteristic zero form with Z-coefficients in trivial weight, we have a hope of attaching an elliptic curve via Taylor’s theorem [78].”
- Paramodular Abelian Varieties of Odd Conductor (2010, methodology): “For imaginary quadratic fields, work of Cremona and his students combined with [63] suggests modularity there as well.”
- Nearly ordinary Galois deformations over arbitrary number fields (2007, methodology): “Presumably one could prove the association between f and E using the methods of [39].”