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University of Sydney
School of Mathematics and Statistics
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.
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