Predicting slopes of modular forms and reductions of crystalline representations

Abstract: 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.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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