Learning Seminar on Emerton-Gee stacks
Fall 2022
Organizers: Daniel Le, Tong Liu
Class number for registration: CRN 31039
Lectures:
- Thursday 3-4 pm, Math 731
Announcements
Sep. 1st The first talk is given by Daniel Le
Sept. 8th The second talk is given by Nicolas Diaz-Wahl
Sept. 15th June Weiland will discuss (φ, Γ)-modules for general coefficents
Sept. 22nd Yifu Wang will discuss generality of stack
Sept. 29th Shiang Tang will discuss formal algebraic stack
Oct. 6th Christian Hokaj will discuss stack of φ -modules
Oct. 13th Tong Liu will discuss properties stack of φ -modules, like Ind-algebraic
Oct. 20th Shiang Tang will discuss the construction of stack of(φ, Γ) -modules and properties of weak Wach modules
Oct. 27th Daniel Le will discuss the indi-algebraicity of stack of(φ, Γ) -modules
Tentative topics and shedule:
- Introduction (Daniel Le)
- Galois representation and (φ, Γ)-modules (Nicolas Diaz-Wahl & June Weiland)
- Stacks (Yifu Wang & Shiang Tang)
- Stacks of φ-modules (Christian Hokaj & Tong Liu )
- Stacks of (φ, Γ)-modules (Shiang Tang & Daniel Le )
- Crystalline stacks (Nicolas Diaz-Wahl & Christian Hokaj )
- Herr complex (Luming Zhao )
- crystalline lift (Tong Liu )
Resources and useful links:
Moduli stacks of etale (phi,Gamma)-modules and the existence of crystalline lifts
Moduli stacks of (phi,Gamma)-modules: a survey
John Voight's note on stacks
Jarod Alper's course on stacks
Emerton and Gee's paper: "
scheme-theoretic images" of morphisms of stacks
Pappas & Rapoport's paper: Phi-modules and coefficient spaces
Aug. 24th, 2022