Seminar on syntomic cohomology and related topics

Organisers: Giovanni Rosso and Ju-Feng Wu

Time: First series of talks at 9:00; second and third series of talks at 14:00.

The seminar consists of three parts:

  1. Ting-Han will give the first series of talks. There will be 8 talks in this part and the talks will focus on three papers by A. Besser ([Bes00a; Bes00b; Bes00c]).

  2. Ju-Feng will give the second series of talks. There will be 6 talks and the talks attempt to understand the paper by P. Colmez, G. Dospinescu and W. Nizioł ([CDN20]) as well as some related topics ([Lur09a; Lur09b; Gle20; Vez18]).

  3. Martí will give a talk about L-invariants and Hyodo--Kato cohomology by following the paper by A. Besser and E. de Shalit ([BdS16]).

First series of talks:

Talk 1.1 (25. May.): Syntomic regulators and p-adic integration

Talk 1.2 (01. Jun.): Syntomic regulators and p-adic integration, Cont'd

Talk 1.3 (08. Jun.): Syntomic regulators and p-adic integration, Cont'd

(15. Jun) [No seminar]

Talk 1.4 (22. Jun.): Coleman integral and finite polynomial cohomology

Talk 1.5 (29. Jun.): Coleman integral and finite polynomial cohomology, Cont'd

Talk 1.6 (06. Jul.): Coleman integral and finite polynomial cohomology, Cont'd

Second and third series of talks:

Talk 2.1 (27. May.): A crash course on derived ∞-categories

Talk 2.2 (03. Jun.): Specialisation maps and dagger spaces in modern fancy languages

Talk 2.3 (10. Jun.) [start at 14:30]: Overconvergent Hyodo–Kato cohomology

Talk 2.4 (17. Jun.): Overconvergent syntomic cohomology

(24. Jun.): [No seminar]

Talk 2.5 (30. Jun., Wed.): Crystalline syntomic cohomology

Talk 2.6 (08. Jul.): The fundamental diagram

Talk 3.1 (14. Jul., Wed.): L-invariants of p-adically uniformised varieties


Notes

The seminar notes are here.

References

[BdS16] Amnon Besser and Eude de Shalit. L-invariants of p-adically uniformized varieties. Annales mathématiques du Québec 40 (2016)

[Bes00a] Amnon Besser. Syntomic regulators and p-adic integration I, Rigid syntomic regulators. Israel Journal of Mathematics 120 (2000)

[Bes00b] Amnon Besser. Syntomic regulators and p-adic integration II, K_2 of curves. Israel Journal of Mathematics 120 (2000)

[Bes00c] Amnon Besser. A generalization of Coleman’s p-adic integration theory. Inventiones mathematicae 142 (2000)

[CDN20] Pierre Colmez, Gabriel Dospinescu, and Wiesława Nizioł. Cohomology of p-adic Stein spaces. Inventiones mathematicae 219 (2020)

[Gle20] Ian Gleason. Specialization maps for Scholze's category of diamonds. Preprint. Available at: https://arxiv.org/abs/2012.05483. 2020

[Lur09a] Jacob Lurie. Derived Algebraic Geometry I: Stable ∞-Categories. Preprint. Available at: http://people.math.harvard.edu/~lurie/papers/DAG-I.pdf. 2009.

[Lur09b] Jacob Lurie. Higher Topos Theory. Annals of Mathematics Studies 170, Princeton University Press, 2009.

[Vez18] Alberto Vezzani. The Monsky--Washnitzer and the overconvergent realizations. International Mathematics Research Notices 11 (2018)