Speaker :	Tzu-Jan Li (Academia Sinica)
Title :	Learning Seminar on Integral Hecke Algebras: finiteness on the group side
Time :	2023-05-30 (Tue) 14:00 - 16:00
Place :	Seminar Room 638, Institute of Mathematics (NTU Campus)
Abstract:	For a $p$-adic reductive group $G$, assuming properties of the Fargues-Scholze morphism from the excursion algebra of the dual of $G$ to the Bernstein center of $G$, we shall show that every finitely generated smooth $R[G]$-module is $\mathfrak{Z}$-finite in the sense of Dat-Helm-Kurinczuk-Moss, where $R$ is a noetherian $\mathbb{Z}_\ell$ algebra with $\ell\neq p$. This result will lead to finiteness results for the Hecke algebras of $G$.