Student Arithmetic Seminar

A Galois representation is a representation of some Galois group as linear automorphisms of a module over a ring. One natural source of such representations is the Galois action on the cohomology of algebraic varieties; more simply, one might try to linearize the Galois action on the rational points of an algebraic variety; the simplest example of this kind would be the faithful representation of the Galois group of a polynomial as a group of permutation matrices. I will discuss these Galois representations and those associated to elliptic curves. I will try to indicate some arithmetic information that can be derived from these representations.

A passing familiarity with elliptic curves and some basic notions from representation theory of finite and compact groups should suffice for most of this talk. Speaker(s): Kannappan Sampath (University of Michigan)