Learning Seminar on BMS2

Learning Seminar on BMS2 (Spring 2020)

Logistics

Time: 2:30 pm - 4:00 pm on Fridays
Location: Mason Hall 2330

This semester Shubhodip Mondal and I are organizing a learning seminar on (part of) Bhatt--Morrow--Scholze's work on integral p-adic Hodge theory.

Please email Shubhodip or me if you would like to join the mailing list for this seminar.

This seminar is succeeded by its continuation here.

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.
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.
More to be added...

Tentative Plan

The seminar is divided into two parts. The first part concerns Sections 2-5 of [BMS19] (and relevant background), culminating in appreciation of Thm 1.17 of loc. cit. The second part aims at introducing relevant background for analogous concepts with a "topological" prefix, and hopefully by the end we get to the construction of the complex AΩ via THH.

Schedule

	Date	Speaker	Topic	References
Lecture 1	January 10th	Shizhang Li	Introduction and Organization
Lecture 2	January 17th	Bhargav Bhatt	Hochschild Homology (and its various cousins)
Lecture 3	January 24th	Ruian Chen	Simplicial and ∞-categories
Lecture 4	January 31st	Andy Jiang	Cotangent complex
Lecture 5	February 7th	Lukas Scheiwiller	Derived de Rham complex
Lecture 6	February 13th Location: 2866 East Hall *	Jakub Witaszek	Flat descent of cotangent complex and HH	[BMS19, §3]
Lecture 7	February 21st	Emanuel Reinecke	Quasi-syntomic site	[BMS19, §4]
Lecture 8	February 28th	Shizhang Li	Negative cyclic homology and de Rham cohomology	[BMS19, §5]
Lecture 9	March 27th	Shubhodip Mondal	What is... an E_{\infty} ring spectrum, really? Introduction to THH
Lecture 10	April 3rd	Haoyang Guo	THH over perfectoid base rings	[BMS19, §6]
Lecture 11	April 10th	Shubhodip Mondal	Tate construction	[NS18, §3.1-3.3,4.1] [Oberwolfach Report, P. 825-844]
Lecture 12	April 17th	Attilio Castano	p-adic Nygaard filtration	[BMS19, §7.1-7.3]

* non-standard time or location

!! Starting at Lecture 9, we transit to online seminar style.

Last updated: March 17th, 2020.

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