Introduction:

The Mini-conference on p-adic Langlands program is organized by Yiwen Ding (BICMR), Yongquan Hu (MCM), Liang Xiao (BICMR). It will be held at both BICMR Jiayibing lecture hall (August 16th) and MCM 110 (August 17th). Please see the website for more information on August 16th.

Time:

2023.8.17 (Thursday)

Place:

MCM110

Schedule:

9:00-10:00  Shanxiao Huang (Peking University)

Title: Paraboline Varieties and Associated Eigenvarieties

Abstract: We construct and study paraboline varieties, which interpolate succeesive extensions of deRham (phi,Gamma)-modules (up to twist by characters) of certain type.  On the automorphic side, we construct relative eigenvarieties, and prove the existence of some local-global compatible morphisms between them.

10:30-11:30  Zhixiang Wu (Muenster Universtiy)

Title: Coherent sheaves on the stack of trianguline (varphi, Gamma)-modules

Abstract: I will talk about analytic part of the categorical p-adic Langlands program of Emerton-Gee-Hellmann and joint work in progress with Eugen Hellmann on verifying some expectations for GL_2(Q_p).

13:00-14:00  Benchao Su (Peking University)

Title: Locally $\sigma$-analytic vectors in the completed cohomology of unitary Shimura curves

Abstract: Let $p$ be a prime number, and let $L$ be a finite extension of $\mathbb{Q}_p$. Let $E$ be a sufficiently large finite extension of $\mathbb{Q}_p$, and let $\Sigma$ be the set of $\mathbb{Q}_p$-embeddings of $L$ into $E$. Let $\sigma\in\Sigma$ be a fixed embedding of $L$ into $E$. We employ the methods introduced by Lue Pan to investigate the locally $\sigma$-analytic vectors in the completed cohomology of unitary Shimura curves with coefficients in $E$ attached to a unitary group with a $\mathrm{GL}_2(L)$-factor at $p$. As some applications, we prove a classicality result on regular $\sigma$-de Rham representations appear in the locally $\sigma$-analytic vectors of the completed cohomology of unitary Shimura curves. In this case, we also provide a geometric description of the locally $\sigma$-analytic representation attached to the Galois representation. This is a joint work with Tian Qiu.

14:30-15:30  Yiwen Ding (Peking University)

Title: Change of weights for locally analytic representations of GL2(Qp)

Abstract: Let D’ subset D be rank two (phi, Gamma)-modules, and pi(D’), pi(D) be the associated locally analytic GL2(Qp)-representations. We describe the relation between pi(D’) and pi(D).

16:00-17:00  Bin Zhao (Capital Normal University)

Title: Refined spectral halo for eigencurves 

Abstract: Coleman-Mazur-Buzzard-Kilford conjecture predicted that over the boundary of the weight space, the eigencurve is a disjoint union of rigid analytic spaces which are finite flat over the weight space. This conjecture has been proved by the work of Liu-Wan-Xiao and Diao-Yao. In this talk, I will explain a joint work in progress with Yongquan Hu and Liang Xiao on a refinement of this conjecture and how it can be used to determine the p-adic slopes of all the crystabelline lifts of a reducible (local) mod p Galois representation. The new ingredient is a universal principal series type theory that interpolates classical principal series types.