Date:
December 22 (Thu) 10:00 - December 23 (Fri) 12:10
Place:
This workshop is held in a hybrid form (Onsite + Zoom).
Lecture room (Onsite):
Department of Mathematics, Kyoto University
North campus, Graduate School of Science Bldg. No.3
Lecture room 3-152
Zoom:
Zoom meeting ID: 821 1517 9917
Passcode: ????? (The largest known Fermat prime (5 digits))
Speakers:
Katsuyuki Bando (Tokyo)
Laurent Fargues (IMG-PRG, Tokyo) (Number Theory Seminar at Kyoto University)
Ildar Gaisin (Kyoto, RIMS)
Kazuhiro Ito (Kavli IPMU)
Teruhisa Koshikawa (Kyoto, RIMS)
Masao Oi (Kyoto, Department of Mathematics)
Teppei Takamatsu (Kyoto, Department of Mathematics)
Organizer:
Tetsushi Ito (Kyoto, Department of Mathematics)
Support:
This workshop is supported by KAKENHI (Grants-in-Aid for Scientific Research) 21H00973.
To prevent the spread of COVID-19:
Registration is mandatory. All the participants of the workshop should register.
The participants should keep a safe distance from others.
The participants should wear a mask in the lecture room.
The participants should use an alcohol-based hand sanitizer.
The participants should not eat or drink in the lecture room, except for appropriate hydration.
The participants should not talk loudly.
The participants should stay home if they feel unwell.
Program
December 22 (Thu)
10:00-11:00 Gaisin
11:10-12:10 Koshikawa
14:00-15:00 Ito (Zoom)
15:15-16:15 Bando
December 23 (Fri)
10:00-11:00 Takamatsu
11:10-12:10 Oi
13:30-14:30 Fargues (Number Theory Seminar at Kyoto University)
Titles & Abstracts
December 22 (Thu)
10:00-11:00 Ildar Gaisin (Kyoto, RIMS)
Title: Revisiting the specialization morphism
Abstract:Basically by Raynaud the specialization morphism from the rigid analytic fiber to it's formal model is ``proper". I want to make this precise and also discuss ``compactifications" of morphisms from a rigid space down to a scheme. Warning: this talk is about some classical ``finite-type" rigid geometry, so I apologize if it is boring :)
11:15-12:15 Teruhisa Koshikawa (Kyoto, RIMS)
Title: On the generic part of the cohomology of locally symmetric spaces
Abstract: Caraiani-Scholze proved certain vanishing theorems for the cohomology of unitray Shimura varieties. I will talk about some conjectures and results about the generic part of the cohomology of locally symmetric spaces.
14:00-15:00 Kazuhiro Ito (Kavli IPMU) (Zoom)
Title: G-displays over prisms and deformation theory
Abstract: The notion of display, which was introduced by Zink, has been successfully applied to the deformation theory of p-divisible groups. Recently, for a reductive group G over the ring of p-adic integers, Lau introduced the notion of G-display. In this talk, following the approach of Lau, we study displays and G-displays over the prismatic site of Bhatt-Scholze, and explain the deformation theory for them.
We also discuss two applications: a conjecture of Pappas-Rapoport on the local representability of unramified integral local Shimura varieties, and an alternative proof of the classification of p-divisible groups over a complete discrete valuation ring of mixed characteristic (0, p) with perfect residue field.
15:15-16:15 Katsuyuki Bando (Tokyo)
Title: Relation between the two geometric Satake equivalence via nearby cycle
Abstract: Fargues and Scholze proved the geometric Satake equivalence over the Fargues-Fontaine curve. On the other hand, Zhu proved the geometric Satake equivalence using a Witt vector affine Grassmannian. In this talk, I will explain the relation between the two version of the geometric Satake equivalence via nearby cycle.
December 23 (Fri)
10:00-11:00 Teppei Takamatsu (Kyoto, Department of Mathematics)
Title: On the structure of semi-infinite Deligne-Lusztig varieties and affine Deligne-Lusztig varieties for GSp
Abstract: The Deligne-Lusztig theory is a theory that realizes the representation of finite reductive groups on the l-adic cohomologies of some varieties, so-called Deligne-Lusztig varieties (DLV for short). Lusztig expected that similar constructions work over p-adic fields. On the other hand, there are two known analogues of DLV over p-adic fields: semi-infinite DLV and affine DLV. Recently, Chan-Ivanov gave a linear-algebraic description of both analogues for GLn, and they proved that semi-infinite DLV can be written as an inverse limit of affine DLV. Moreover, as an application, they studied the detailed structure of affine DLV, and they also confirmed Lusztig's expectation. In this talk, I want to explain the analogue of Chan-Ivanov's result for GSp.
11:10-12:10 Masao Oi (Kyoto, Department of Mathematics)
Title: On B(G)-parametrization of the local Langlands correspondence
Abstract: According to Vogan's philosophy, it is expected that the local Langlands correspondence can be formulated in a better way if we simultaneously treat some class of inner forms. One possible choice of such a class is the class of inner forms arising from basic isocrystals. In this talk, I will explain that we can formulate and construct a local Langlands correspondence for all isocrystals by assuming that for basic isocrystals in a reasonable way. This talk is based on my joint work with Alexander Bertoloni Meli (University of Michigan).