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.

If you would like to be included in the mailing list or have any questions or comments, please send me an email at m.leonhardt@dpmms.cam.ac.uk.

Schedule

  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: Cherednik-Drinfeld Theorem - -adic uniformization (Zhiyou)

Past Reading groups

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.

Schedule

-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.