A note on some -adic analytic Hecke actions
Lue Pan
Princeton University, Princeton, USA
![A note on some $p$-adic analytic Hecke actions cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserials%2Fcover-jems.png&w=3840&q=90)
Abstract
We show that the action of Hecke operators away from on the space of (-adic) overconvergent modular forms is (-adically) locally analytic in a certain sense. As a corollary, the action of the Hecke algebra can be extended naturally to an action of rigid functions on its generic fiber. This directly determines the Hodge–Tate–Sen weights of Galois representation associated to an overconvergent eigenform and confirms a conjecture of Gouvêa.
Cite this article
Lue Pan, A note on some -adic analytic Hecke actions. J. Eur. Math. Soc. (2024), published online first
DOI 10.4171/JEMS/1433