Topological Hochschild Homology and L-functions

Specialeforsvar ved Guillem Sala Fernandez

Titel: Topological Hochschild Homology and L-functions

Abstract: We update Lars Hesselholt’s paper “THH and the Hasse-Weil Zeta Function” [Hes16] by following the language of Topological Cyclic Homology developed By Nikolaus-Scholze in [NS17] and using a variety of results from Bhatt-Morrow-Scholze’s “THH and Integral p-adic Hodge Theory” [BMS18]. More precisely, we give a shorter explanation of Hesselholt’s cohomological interpretation of the Hasse-Weil Zeta function by means of the Bhatt-Morrow-Scholze filtration, which gives rise to a spectral sequence computing Topological periodic cyclic homology in terms of crystalline cohomology, and update Hesselholt’s construction of the divided Bott element using recent results by Clausen-Mathew-Morrow in [CMM18] and the description of TC(OC; Zp) by Hesselholt-Nikolaus in [HN19], where OC is the ring of integers of C, a complete and algebraically closed extension of the p-adic rational numbers Qp. 

Vejleder: Ryomei Iwasa
Censor:   Martin Raussen, Aalborg Universitet