Continuing Seminar on BMS2 and surrounding topics (Summer 2020)
Logistics
Time: Friday 14:3016:00
Location: Zoom
This is a continuation of our previous seminar on integral padic 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 Ktheory untouched).
After that, assuming there are remaining momentum, we can start learning a relevant topic, for instance, chapters 811 of [BMS19] (think of as 4 topics, interrelated of course), relation to prismatic cohomology, or [AMMN20, Sections 56] (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, padic 
[BMS19, §6] 
Lecture 4 
May 15th 
Haoyang Guo 
padic Nygaard complexes, I 
[BMS19, §7.17.2] 
Lecture 5 
May 22nd 
Haoyang Guo 
padic Nygaard complexes, II 
[BMS19, §7.27.3] 
Lecture 6 
May 29th 
Shubhodip Mondal 
Tate diagonal 
[NS18, §III] 
Lecture 7 
June 5th 
Andy Jiang 
Relative THH and BreuilKisin 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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