Loading Events

Slopes of modular forms and reductions of crystalline representations

SEMINARS: NUMBER THEORY

When: April 27, 2022
3:00 pm - 4:00 pm
Where: Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138, United States
Speaker: 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.