Number Theory Seminar: Slopes of modular forms and reductions of crystalline representations
SEMINARS, NUMBER THEORY
Robert Pollack - Boston University
The ghost conjecture predicts slopes of modular forms whose residual representation is locally reducible. In this talk, we'll examine locally irreducible representations and discuss recent progress on formulating a conjecture in this case. It's a lot trickier and the story remains incomplete, but we will discuss how an irregular ghost conjecture is intimately related to reductions of crystalline representations.