**Prismatization seminar**

The goal of this seminar is to understand Drinfeld's prismatization paper with an eye towards F-gauges, as well as some related papers and applications.

Thursdays 11:30 AM - 1 PM, 528 Mathematics

[1] Bhargav Bhatt and Jacob Lurie. "Absolute prismatic cohomology." *arXiv preprint arXiv:2201.06120* (2022).

[2] Bhargav Bhatt and Jacob Lurie. "The prismatization of p-adic formal schemes." *arXiv preprint arXiv:2201.06124* (2022).

[3] Bhargav Bhatt and Peter Scholze. "Prisms and prismatic cohomology." *arXiv preprint arXiv:1905.08229* (2019).

[4] Vladimir Drinfeld. "Prismatization." *arXiv preprint arXiv:2005.04746* (2020).

Date |
Speaker |
Topic |
References |
Notes |

September 8 | Avi Zeff | Introduction, organization and overview | [1, 2, 3, 4] | |

September 15 | Avi Zeff | Overview of prismatic cohomology | [3] | |

September 22 | Ivan Zelich |
Perfectoid rings and THH Perfectoid rings and THH
Cyclic homology offers, as shown by Connes, a way to refine de Rham cohomology to the non-commutative setting. To unpack what this means, we will delve into the classical theory of Hochschild cohomology with an emphasis on its relation to perfect rings. The modern view point on this theory, afforded by recent developments in homotopy theory, is to consider topological variants, where the theory can be generalised to more homotopically enriched categories. It is possible, in this setting, to perform analogous computations for perfect rings in characteristic p, like in the classical case. If one is to take the analogy that perfectoid rings are characteristic 0 analogues of perfect rings in characteristic p seriously, then one would expect that similar computations can be undertaken for perfectoid rings that would yield similar results. We will attempt to survey such results, and in particular, outline how perfectoid rings can arise as certain Thom spectra. |
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September 29 | Ivan Zelich | Perfectoid rings and THH, continued | ||

October 6 | ||||