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BIMSA-YMSC Tsinghua Number Theory Seminar
BIMSA-YMSC Tsinghua Number Theory Seminar
The p-adic monodromy theorem for families over relatively discrete algebras
The p-adic monodromy theorem for families over relatively discrete algebras
Organizers
Hansheng Diao
, Heng Du
, Yueke Hu
, Huajie Li
, Bin Xu
, Yihang Zhu
Speaker
Yutaro Mikami
Time
Monday, June 1, 2026 10:00 AM - 11:00 AM
Venue
Shuangqing-C654
Abstract
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.