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.
|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|