Learning Seminar on Emerton-Gee stacks
Fall 2022

Basic information

Organizers: Daniel Le, Tong Liu

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The quadratic formula for \(ax^2 + bx + c = 0\) is \[x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}\] which is a standard result in algebra.

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:

  1. Introduction (Daniel Le)
  2. Galois representation and (φ, Γ)-modules (Nicolas Diaz-Wahl & June Weiland)
  3. Stacks (Yifu Wang & Shiang Tang)
  4. Stacks of φ-modules (Christian Hokaj & Tong Liu )
  5. Stacks of (φ, Γ)-modules (Shiang Tang & Daniel Le )
  6. Crystalline stacks (Nicolas Diaz-Wahl & Christian Hokaj )
  7. Herr complex (Luming Zhao )
  8. 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