Effective and minimal cones of weights for Hilbert modular forms (joint with P. Kassaei)

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• Fred Diamond (KCL)
• Tuesday 03 June 2025, 13:00-14:00
• MR12.

If you have a question about this talk, please contact Jef Laga.

I’ll discuss some generalizations of the well-known fact that there are non non-zero modular forms of negative weight, even when working in characteristic p. In particular, for Hilbert modular forms associated to a totally real field of degree d, the weight is a d-tuple, all components of which are non-negative, if working in characteristic zero. But there are mod p Hilbert modular forms, called partial Hasse invariants, whose weight in some component is negative. I’ll explain joint work with Kassaei (from 2017/2020) that shows the possible weights of non-zero Hilbert modular forms in characteristic p lie in the cone generated by the weights of these partial Hasse invariants. In fact we prove a stronger result (motivated by the relation with Galois representations) which asserts that any form whose weight lies outside a certain minimal cone is divisible by a partial Hasse invariant. I’ll also discuss a recent generalization of these results to forms on Goren-Oort strata of Hilbert modular varieties.

This talk is part of the Number Theory Seminar series.

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