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Shu Sasaki: A Serre weight conjecture for mod p Hilbert modular forms

Time: Wed 2021-03-10 13.15 - 14.15

Location: Zoom, meeting ID: 685 0671 8075

Participating: Shu Sasaki, Queen Mary University London

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Abstract 

A Serre weight conjecture for mod p Hilbert modular forms Abstract: In 1987, J.P. Serre formulated a set of conjectures about weights and levels of odd two-dimensional modular mod p representations of the absolute Galois group of Q. Serre's conjecture itself was proved by Khare and Wintenberger in 2009, but it has also inspired a good deal of new mathematics. One strand of research spurred on by this development is an attempt to generalise Serre's conjecture to the setting where we have a totally real number field in place of Q; and it was in the work of Buzzard, Diamond and Jarvis in 2010 that the very first attempt was made (while focusing exclusively on *regular* weight). In my joint work with Diamond, we improve on the BDJ conjecture and formulate new conjectures about (geometric) mod p Hilbert modular forms of *general* weight. In this talk aimed primarily at non-experts, I will explain what these conjectures say (the task still involves a fair amount of algebraic geometry and modular representation theory) and why we, number theorists, should care about them, while at the same time demonstrate some evidence that our conjecture are not just hunches.

Note: The passcode was sent to the AG and NT mailing lists. If you're not on these lists and would like to attend, or are having trouble accessing the meeting, please email Wushi Goldring at wgoldring@math.su.se . To be added to the AG mailing list, please email Jonas Bergström at jonasb@math.su.se .