New Structures and Techniques in $p$-adic Geometry

Collection New Structures and Techniques in $p$-adic Geometry

Organisateur(s) Dustin Clausen, Toby Gee, Wiesława Nizioł
Date(s) 27/10/2025 - 31/10/2025
URL associée https://indico.math.cnrs.fr/event/14073/
00:00:00 / 00:00:00
14 18

Towards mod $p$ Local Global Compatibility for Partial Weight one Hilbert Modular Forms

De Kalyani Kansal

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 ${\rm Gal}(Fp/F)$. 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.

Informations sur la vidéo

  • Date de captation 30/10/2025
  • Date de publication 04/11/2025
  • Institut IHES
  • Langue Anglais
  • Audience Chercheurs
  • Format MP4

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