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Texas A&M Number Theory Seminar

Department of Mathematics
Milner 216
Wednesdays, 1:45-2:45 PM

Margaret Upton

Texas A & M University

Wednesday, February 13, 2008

Milner 216, 1:45PM

Title: Galois Representations Attached to Picard Curves

Abstract: Abstract: Among the most studied objects in current number theory are Galois groups and their associated representations. Much progress in modern number theory, including the proof of the former Shimura-Taniyama conjecture which resulted in the proof of Fermat's Last Theorem, has depended on a detailed understanding of these types of representations.

A classic result of Serre is that the image of the ℓ-adic Galois representation naturally arising from an elliptic curve has image as large as possible for almost all primes ℓ. Extensions of this result are of great interest and under development. I extended this result to a rank 3 case. In this talk, I will explain the background and the methods.