On the cyclotomic t-structure and filtrations on topological Hochschild homology

Specialeforsvar ved Jonas Bastian Vedersø McCandless

Titel:  On the cyclotomic t-structure and filtrations on  topological Hochschild homology

Abstract: We construct the Bhatt--Morrow--Scholze filtration on topological Hochschild homology and its variants and show that the graded pieces are given by certain completed prismatic complexes. Using the recently developed prismatic cohomology of Bhatt and Scholze we recover crystalline cohomology from the graded pieces of the Bhatt--Morrow--Scholze filtration in characteristic p. Moreover, we introduce a t-structure on cyclotomic spectra and explain how to recover crystalline cohomology from topological periodic cyclic homology using this t-structure

Vejleder: Lars Hesselholt
Censor:   Lisbeth Fajstrup, AAU