Speaker: Kalyani Kansal
Affiliation: Imperial College
Title of Talk: Towards mod $p$ local global compatibility for partial weight one Hilbert modular forms
Date: December 17, 2025
Time: 16:00:00 Hours
Venue: AG-77

Abstract: Let $p > 5$ be a prime, and let $F$ be a totally real field in which $p$ is unramified. We study mod $p$ Hilbert modular forms for $F$ of level prime to $p$ and weight $(k, l)$, where $k$ and $l$ are tuples of integers. To a mod $p$ Hilbert modular Hecke eigenform of weight $(k, l)$, Diamond and Sasaki associate a two-dimensional mod $p$ Galois representation of $\mathrm{Gal}(\overline{F}/F)$. The local--global compatibility (LGC) conjecture predicts that, at each place above $p$, the restriction of this representation admits crystalline lifts with Hodge--Tate weights determined explicitly by $(k, l)$. In this talk, we will discuss a proof showing that LGC for regular $p$-bounded weights (each entry of $k$ between $2$ and $p+1$) implies LGC in the partial weight one $p$-bounded case (each entry of $k$ between $1$ and $p+1$). Our approach combines computations of scheme-theoretic intersections on the Emerton--Gee stack with weight-changing arguments on quaternionic Shimura varieties, using restriction to Goren--Oort strata. This is joint work in progress with Brandon Levin and David Savitt.