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On the geometric Serre weight conjecture for Hilbert modular forms

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  • UserSpeaker to be confirmed
  • ClockTuesday 04 March 2025, 14:30-15:30
  • HouseMR13.

If you have a question about this talk, please contact Rong Zhou .

Let $F$ be a totally real field in which $p$ is unramified and $\rho: \Gal(\overline{F}/F)\rightarrow \GL_2(\Fpbar)$ be a totally odd, irreducible, continuous representation. The geometric Serre weight conjecture formulated by Diamond and Sasaki can be viewed as a geometric variant of the Buzzard-Diamond-Jarvis conjecture, where they have the notion of geometric modularity in the sense that $\rho$ arises from a mod $p$ Hilbert modular form and algebraic modularity in the sense of Buzzard-Diamond-Jarvis. I will discuss the relation between algebraic and geometric modularity and show their consistency for the weights in a certain cone, under the assumption that $F$ is a real quadratic field.

This talk is part of the Number Theory Seminar series.

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