Arithmetic Geometry Reading Seminar


Spring semester 2023 - Thursday 16:00 - 18:30

The goal of this seminar is to understand Scholze's proof of the weight-monodromy conjecture [1]. We mainly follow the notes by Bhargav Bhatt [2].



List of the talks
  1. (01/03, HG E23) Organisational Meeting
  2. (09/03, HG G19.2, Beat) Introduction to the weight-monodromy conjecture [1], [3]
  3. (16/03, HG G19.2, Neeraj) Conventions and perfectoid fields [2, Chapter 1 - 3]
  4. (23/03, HG G19.2, Aitor, 15:00 - 17:30) Almost commutative algebra [2, Ch. 4]
  5. (30/03, HG G19.2, Dmitry) Banach algebras and perfectoid algebras [2, Ch. 5 - 6]
  6. (06/04, HG G19.2, Tim) Adic spaces [2, Ch. 7]
  7. (20/04, HG G19.2, Tim) Adic spectrum via algebraic geometry [2, Ch. 8]
  8. (27/04, HG G19.2, Beat) Toric varieties, toric varieties in the perfectoid world
  9. (04/05, HG G19.2, Felix) Perfectoid spaces [2, Ch. 9]
  10. (11/05, HG G19.2, Felix) Perfectoid spaces [2, Ch. 9]
  11. (25/05, HG G19.2, Dmitry) The almost purity theorem [2, Ch. 10]
  12. (01/06, HG G19.2, Beat, 13:00 - 15:30) The weight-monodromy conjecture [1]


References
[1] Perfectoid Spaces, Peter Scholze, 2011, Link.
[2] Lecture notes for a class on perfectoid spaces, Bhargav Bhatt, 2017, Link.
[3] La conjecture de Weil : II, Pierre Deligne, Publications Mathématiques de l'IHÉS, Volume 52 (1980), pp. 137-252, Link.