MCM-YMSC p-adic Geometry Learning Seminar (Fall 2022)

that is the question


Organizers: Koji and Shizhang
Time: Monday 14:00--15:30
Location: MCM 110

This is a learning seminar on Banach--Colmez spaces.

Please email Shizhang if you would like to join the mailing list for this seminar.


Tentative Plan

The goal of this series of talks is to learn the basics of finite-dimensional Banach Spaces (aka. Banach--Colmez spaces). More details can be found here. There is a small chance we might have to deviate from this schedule if some topics end up taking longer/shorter than we expect.


Here are some (handwritten) notes: Lecture 2, Lecture 3, Lecture 4, Lecture 5, Lecture 6, Lecture 7, Lecture 8, Lecture 10, Lecture 11, Lecture 12, Lecture 13, Lecture 14, and Lecture 15.

Schedule (roughly)

  Date  Speaker  Topic  References 
Lecture 1  September 5th  Koji Shimizu  Introduction and organization  [Col02, Introduction] 
Lecture 2  September 19th  Shizhang Li  Sympathetic algebras and \widehat{\overline{C\{X\}}}  [Col02, §2-3] 
Lecture 3  September 26th  Yongquan  Sympathetic closure  [Col02, §5] 
Lecture 4  October 10th  Qijun  A funny field \mathfrak{C}  [Col02, §4, 6.1-6.5] 
Lecture 5  October 17th  Yupeng  Vector Spaces  [Col02, §6.6-6.9, 7.1-7.2] 
Lecture 6  October 24th  Zhefan  Finite-dimensional Banach Spaces  [Col02, §7.3-7.8] 
Lecture 7  October 31st  Daxin  p-adic period rings  [Col02, §8] 
Lecture 8  November 7th  Yong-Suk  Fundamental exact sequence  [Col02, §9] 
Lecture 9  November 14th  Zekun  weakly admissible implies admissible  [Col02, §11] 
Lecture 10  November 21st  Jiedong  Banach--Colmez spaces  [LB18, §2] 
Lecture 11  November 28th  Ruochuan  Pro-étale cohomology of affine spaces  [LB18, §3] 
Lecture 12  December 5th  Heng  The category \mathscr{BC} in terms of
the Fargues--Fontaine curve 
[LB18, §5-7] 
Lecture 13  December 12th  Koji  Overview and local syntomic computations  [CN17, §1-3] 
Lecture 14  December 19th  Shanwen  Syntomic cohomology and (\phi, \Gamma)-modules  [CN17, §4] 
Lecture 15  December 26th  Yong-Suk  Semistable comparison theorem  [CN17, §5] 

Last updated: December 27th, 2022.

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