Continuing Seminar on BMS2 and surrounding topics (Summer 2020)
Logistics
Time: Friday 14:30--16:00
Location: Zoom
This is a continuation of our previous seminar on integral p-adic Hodge theory.
Please email me if you would like to join the mailing list for this seminar.
This seminar is succeeded by a seminar on a universal HKR theorem.
References
- Bhargav Bhatt, Matthew Morrow, and Peter Scholze, Topological Hochschild homology and integral p–adic Hodge theory, Publ. Math. Inst. Hautes Études Sci.129(2019),199–310. MR 3949030, arXiv.
- Bhargav Bhatt and Peter Scholze, Prisms and prismatic cohomology
- Thomas Nikolaus and Peter Scholze, On topological cyclic homology, Acta Math.221(2018), no. 2, 203–409. MR 3904731, arXiv.
- Lars Hesselholt and Thomas Nikolaus, Topological cyclic homology, 2019, Chapter in Handbook of Homotopy Theory.
- Arbeitsgemeinschaft: Topological Cyclic Homology, Oberwolfach Rep.15(2018), no. 2,805–940, Abstracts from the working session held April 1–7, 2018, Organized by Lars Hesselholt and Peter Scholze. MR 3941522.
- Matthew Morrow, Topological Hochschild homology in arithmetic geometry, Morrow's notes from Arizona Winter School in 2019.
- Benjamin Antieau, Akhil Mathew, Matthew Morrow, and Thomas Nikolaus, On the Beilinson fiber square
- More to be added...
Tentative Plan
We'll first learn the cyclotomic structure of THH from various sections of [NS18]. Then we shall finish learning the chapters 6 and 7 of [BMS19] (leaving K-theory untouched).
After that, assuming there are remaining momentum, we can start learning a relevant topic, for instance, chapters 8-11 of [BMS19] (think of as 4 topics, inter-related of course), relation to prismatic cohomology, or [AMMN20, Sections 5-6] (please feel free to email me suggesting topics).
Schedule
|
Date |
Speaker |
Topic |
References |
Lecture 1 |
April 24th |
Shizhang Li |
Frobenius on THH and Organization |
[NS18, §I.4, III.1] |
Lecture 2 |
May 1st |
Shizhang Li |
More on THH, characteristic p |
[NS18, §IV.4] |
Lecture 3 |
May 8th |
Andy Jiang |
Even more on THH, p-adic |
[BMS19, §6] |
Lecture 4 |
May 15th |
Haoyang Guo |
p-adic Nygaard complexes, I |
[BMS19, §7.1-7.2] |
Lecture 5 |
May 22nd |
Haoyang Guo |
p-adic Nygaard complexes, II |
[BMS19, §7.2-7.3] |
Lecture 6 |
May 29th |
Shubhodip Mondal |
Tate diagonal |
[NS18, §III] |
Lecture 7 |
June 5th |
Andy Jiang |
Relative THH and Breuil--Kisin modules |
[BMS19, §11] |
Lecture 8 |
June 12th |
Shizhang Li |
Introduction to prismatic cohomology |
[BS19, §1] |
Lecture 9 |
June 19th |
Emanuel Reinecke |
Comparing with prismatic cohomology |
[BS19, §13] |
Last updated: May 8th, 2020.
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