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Seminar on cyclotomic spectra and Cartier modules

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    
Dec 9 TBD