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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.