Sydney University Algebra Seminar

    University of Sydney

    School of Mathematics and Statistics

    Algebra Seminar

    Helena Verrill
    Cambridge University

    Images of modular mod l Galois representations.

    Friday 25th May, 12-1pm, Carslaw 159.

    Modular forms which are Cusp forms and Hecke Eigen forms give rise to l-adic Galois Galois representations, and taking the forms mod l (l a prime) give rise to representations of the Galois group of Q in GL2(k), where k is some finite extension of the finte field with l elements. Ribet proved that for a given modular form, the corresponding modular mod l Galois representaions almost always have image "as large as possible" in PGL2(k) (i.e., the projectivization of the image). The exceptional cases are where the projective image is cyclic, dihedral, or isomorphic to A4, S4, or A5. I will discuss joint work with Ian Kiming on how to determine and prove when the image is one of the latter 3 types, and give bounds on how large l can be for such an image to occur.