Arithmetic Geometry and Number Theory RTG Seminar: Lifting irreducible Galois representations

Seminar | April 29 | 3-5 p.m. | 748 Evans Hall

 Stefan Patrikis, University of Utah

 Department of Mathematics

A basic question in the study of Galols representations is whether a mod p representation, valued in any reductive group, of the absolute Galois group of a number field admits a geometric p-adic lift. In some cases this question has a positive answer, in other cases a negative answer, and sometimes we simply don't know what to expect. Perhaps the most general setting in which one can hope for a positive result is when the number field is totally real, and the representation in question is "totally odd," generalizing Serre's notion of oddness for GL(2). I will discuss joint work with N. Fakhruddin and C. Khare on finding geometric lifts of irreducible totally odd representations.