Constructing elliptic curves from Galois representations

@article{Snowden2017ConstructingEC,
  title={Constructing elliptic curves from Galois representations},
  author={Andrew Snowden and Jacob Tsimerman},
  journal={Compositio Mathematica},
  year={2017},
  volume={154},
  pages={2045-2054}
}
  • Andrew Snowden, Jacob Tsimerman
  • Published 2017
  • Mathematics
  • Compositio Mathematica
  • Given a non-isotrivial elliptic curve over an arithmetic surface, one obtains a lisse $\ell$ -adic sheaf of rank two over the surface. This lisse sheaf has a number of straightforward properties: cyclotomic determinant, finite ramification, rational traces of Frobenius elements, and somewhere not potentially good reduction. We prove that any lisse sheaf of rank two possessing these properties comes from an elliptic curve. 
    Geometric Properties of Families of Galois Representations
    Rank 2 local systems and abelian varieties.
    5

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 11 REFERENCES
    REMARKS ON A CONJECTURE OF FONTAINE AND MAZUR
    98
    ELLIPTIC MODULES. II
    44
    NÉRON MODELS
    442
    Elliptic Modules
    • 1977
    Langland’s conjecture for GL(2) over function fields
    • 1978
    Rational points. Third edition. Papers from the seminar held at the Max-Planck-Institut für Mathematik, Bonn/Wuppertal, 1983/1984. With an appendix by Wüstholz
    • 1992