- BIMSA-YMSC 清华数论讨论班

The p-adic monodromy theorem for families over relatively discrete algebras

组织者

刁晗生 , 杜衡 , 胡悦科 , ‌李华杰 , 徐斌 , 朱艺航

演讲者

Yutaro Mikami

时间

2026年06月01日 10:00 至 11:00

地点

Shuangqing-C654

摘要

The analytic Emerton-Gee stack is the rigid analytic moduli stack of $(\phi, \Gamma)$-modules over the Robba ring and plays a central role in the formulation of the categorical $p$-adic local Langlands correspondence proposed by Emerton, Gee, and Hellmann. The result of Rodrigues Jacinto and Rodríguez Camargo in the case of $GL_1$ suggests that, as test objects for the analytic Emerton–Gee stack, one should consider algebraic-affinoid $\mathbb{Q}_p$-algebras, which are “combinations of discrete algebras and affinoid $\mathbb{Q}_p$-algebras”. Motivated by this observation, I introduce the families of $(\phi, \Gamma)$-modules parametrized by algebraic-affinoid $\mathbb{Q}_p$-algebras. I then explain how the $p$-adic monodromy theorem for families proved by Berger and Colmez can be generalized to this setting.