Institut für Mathematik


Modul:   MAT770  Oberseminar: Algebraische Geometrie

Log prismatic cohomology, motivic spectra and comparison theorems

Vortrag von Dr. Alberto Merici

Sprecher eingeladen von: Prof. Dr. Joseph Ayoub

Datum: 30.04.24  Zeit: 13.15 - 14.45  Raum: Y27H25

We prove that (logarithmic, Nygaard completed) prismatic and (logarithmic) syntomic cohomologies are representable in the category of logarithmic motives. As an application, we immediately obtain Gysin maps for prismatic and syntomic cohomologies, and we precisely identify their cofibers. In the second part of the talk we develop a descent technique that we call saturated descent, inspired by the work of Niziol on log K-theory. Using this, we prove crystalline comparison theorems for log prismatic cohomology, log Segal conjectures and log analogues of the Breuil-Kisin prismatic cohomology, from which we get Gysin maps for the A_{inf} cohomology.