In the reading seminar this term we will go through the paper:

Antieau and Nikolaus, Cartier modules and cyclotomic spectra, J. Amer. Math. Soc. (2021), no. 1, 1-78

The authors establish a conceptual relationship between the theory of cyclotomic spectra and arithmetic geometry consolidating earlier results of Hesselholt-Madsen and Hesselholt on the relationship between topological Hochschild homology and the Witt vectors and the de Rham-Witt complex. They define a t-structure on the category of p-cyclotomic spectra and identify the heart with the category of Cartier modules, and show that THH of a perfect field belongs to the heart and corresponds to the Cartier module of Witt vectors.

We will meet on Thursday at 5pm during term 1 in MS.03. Here is an outline of the talks, and a more detailed description. Please get in touch if you would like to contribute with a talk.

Date	Talk	Speaker	Notes
Oct 7	Overview	Emanuele Dotto
Oct 14	Equivariant spetra	Emanuele Dotto
Oct 21	Cyclotomic spectra, TR and TC	David Tintinago-Pinzon
Oct 27	The cyclotomic t-structure	Julie Rasmusen
Nov 4	Topological Cartier modules I: Examples	Irakli Patchkoria
Nov 11	Topological Cartier modules II: The t-structure	Andrew Macpherson
Nov 18	Topological Cartier modules and cyclotomic spectra	Emanuele Dotto
Nov 25	The heart	Christopher Lazda
Dec 2	THH of perfect rings	Emanuele Dotto
Dec 9	TBD