Reading Groups

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Past Reading groups

Michaelmas 2017: Drinfeld Upper Half Plane

This term, we want to understand the Drinfeld upper half plane, following a paper by Boutot-Carayol. An English translation of the paper can be found here.


  1. Thursday 19/10/2017, 4pm, MR13: Motivation (Zhiyou); notes
  2. Thursday 26/10/2017, 3pm, MR4: The Bruhat-Tits tree of (Beth)
  3. Thursday 02/11/2017, 4pm, MR13: Formal and functorial versions of the upper half plane (Ben)
  4. Thursday 09/11/2017, 3pm, MR13: Formal -modules and statement of the ‘Basic Theorem’ (Christos); notes
  5. Thursday 16/11/2017, 4pm, MR13: Sketch of proof of the ‘Basic Theorem’ (Axel); notes
  6. Thursday 23/11/2017, 3pm, MR13: Quaternion algebras and Shimura curves (Marius)
  7. Monday 04/12/2017, 3pm, MR13: An application of -adic uniformization to level-lowering (Jack)
  8. Wednesday 06/12/2017, 3pm, MR13: Cerednik-Drinfeld Theorem - -adic uniformization (Zhiyou)

Easter Term 2017: Perfectoid Student Seminar

Picture of the closed adic unit disc

Between May and July 2017, Christos, Zhiyou and I were organising a student-led seminar on -adic Hodge theory and (perfectoid) Shimura varieties. It started off as a way of not-forgetting what Zhiyou and I learned at the Arizona Winter School 2017. We then moved on to working on Scholze’s torsion paper.


-adic Hodge theory

  1. Thursday 04/05/2017, MR14, 4pm: Tate’s “p-divisible groups” (Marius)
  2. Thursday 11/05/2017, MR13, 3pm: The Hodge-Tate Decomposition (Christos)
  3. Thursday 18/05/2017, MR13, 4pm: Primitive Comparison Theorem (Zhiyou)
  4. Thursday 25/05/2017, MR13, 4pm: Fontaine’s results (Gyujin, Leo)
  5. Thursday 08/06/2017, MR13, 3:45pm: Shimura Varieties (Jack)
  6. Thursday 15/06/2017, MR13, 4pm: Variations of Hodge structures (Ben)
  7. Tuesday 20/06/2017, MR13, 2:30pm: Integral p-adic Hodge Theory (Tony)

Scholze’s Torsion paper

  1. Thursday 22/06/2017, MR13, 4pm: Motivation for studying Shimura varieties (Gyujin)
  2. Tuesday 27/06/2017, MR5, 4pm: Introduction to perfectoid spaces (Marius)
  3. Thursday 29/06/2017, MR13, 4pm: Overview (Zhiyou)
  4. Thursday 06/07/2017, MR13, 4pm: Hodge-Tate period business (Christian)
  5. Tuesday 11/07/2017, MR13, 2:30pm: Chapter IV, part 1 (Christos)
  6. Thursday 13/07/2017, MR13, 4pm: Chapter IV, part 2 (Gyujin)
  7. Thursday 20/07/2017, MR13, 4pm: Chapter V, part 1 (Marius)
  8. Thursday 27/07/2017, MR13, 4:30pm: Chapter V, part 2 (Zhiyou)

Exercise Sessions

Alongside the seminar talks, we also had some example sessions where we mostly talked about exercises from the AWS notes.