Number Theory Seminar: Slopes of modular forms and reductions of crystalline representations


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April 27, 2022 3:00 pm - 4:00 pm
Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138 USA

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.