EVENT DETAILS AND ABSTRACT

Title: Even Galois representations and the Fontaine-Mazur conjecture
Speaker: Frank Calegari
Speaker Info: IAS and Northwestern
Brief Description:
Special Note:
Abstract:

What Galois representations "come" from algebraic geometry? The Fontaine-Mazur conjecture gives a very precise conjectural answer to this question. One dimensional representations are well understood by class field theory, and two dimensional representations are usually discussed in relation to classical modular forms. On the other hand, the Galois representations attached to modular forms are odd, that is, the determinant of the image of complex conjugation is -1. What about the even representations? We discuss the conjectural answer to this question, and generalize Kisin's recent work on the Fontaine-Mazur conjecture to the even case.