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Past Reading groups
- Michaelmas 2017: Drinfeld upper half plane and -adic uniformization of Shimura curves (below)
- Easter Term 2017: -adic Hodge theory and Scholze’s torsion paper (below)
- Lent Term 2017: Drinfeld
- Michaelmas Term 2016: The Euler system of Heegner points (based on these notes from Tom Weston)
- Easter Term 2016: Jacquet-Langlands
- Lent Term 2016: Langlands-Kottwitz method (based on Peter Scholze’s master thesis)
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.
- Thursday 19/10/2017, 4pm, MR13: Motivation (Zhiyou); notes
- Thursday 26/10/2017, 3pm, MR4: The Bruhat-Tits tree of (Beth)
- Thursday 02/11/2017, 4pm, MR13: Formal and functorial versions of the upper half plane (Ben)
- Thursday 09/11/2017, 3pm, MR13: Formal -modules and statement of the ‘Basic Theorem’ (Christos); notes
- Thursday 16/11/2017, 4pm, MR13: Sketch of proof of the ‘Basic Theorem’ (Axel); notes
- Thursday 23/11/2017, 3pm, MR13: Quaternion algebras and Shimura curves (Marius)
- Monday 04/12/2017, 3pm, MR13: An application of -adic uniformization to level-lowering (Jack)
- Wednesday 06/12/2017, 3pm, MR13: Cerednik-Drinfeld Theorem - -adic uniformization (Zhiyou)
Easter Term 2017: Perfectoid Student Seminar
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
- Thursday 04/05/2017, MR14, 4pm: Tate’s “p-divisible groups” (Marius)
- Thursday 11/05/2017, MR13, 3pm: The Hodge-Tate Decomposition (Christos)
- Thursday 18/05/2017, MR13, 4pm: Primitive Comparison Theorem (Zhiyou)
- Thursday 25/05/2017, MR13, 4pm: Fontaine’s results (Gyujin, Leo)
- Thursday 08/06/2017, MR13, 3:45pm: Shimura Varieties (Jack)
- Thursday 15/06/2017, MR13, 4pm: Variations of Hodge structures (Ben)
- Tuesday 20/06/2017, MR13, 2:30pm: Integral p-adic Hodge Theory (Tony)
Scholze’s Torsion paper
- Thursday 22/06/2017, MR13, 4pm: Motivation for studying Shimura varieties (Gyujin)
- Tuesday 27/06/2017, MR5, 4pm: Introduction to perfectoid spaces (Marius)
- Thursday 29/06/2017, MR13, 4pm: Overview (Zhiyou)
- Thursday 06/07/2017, MR13, 4pm: Hodge-Tate period business (Christian)
- Tuesday 11/07/2017, MR13, 2:30pm: Chapter IV, part 1 (Christos)
- Thursday 13/07/2017, MR13, 4pm: Chapter IV, part 2 (Gyujin)
- Thursday 20/07/2017, MR13, 4pm: Chapter V, part 1 (Marius)
- Thursday 27/07/2017, MR13, 4:30pm: Chapter V, part 2 (Zhiyou)
Alongside the seminar talks, we also had some example sessions where we mostly talked about exercises from the AWS notes.