P-adic Etale Tate Twists and Syntomic Cohomology

Explore the intricacies of p-adic étale Tate twists and syntomic cohomology in this advanced mathematics lecture delivered by Akhil Mathew from the University of Chicago and Clay Mathematics Institute. Delve into complex topics such as p-quasisyntomic topology, prismatic cohomology, and Cartier smoothness as part of the 2021 Fields Medal Symposium honoring Peter Scholze. Examine the setup, key concepts, and definitions before progressing to comparisons, class of schemes, and regular rings. Conclude with a discussion on the Main Theorem and the Italian Comparison Theorem, gaining insights into cutting-edge research in algebraic geometry and number theory.

Introduction
Setup
Concept
P quasisyntomic
Top degree chromology
Definition
Comparison map
Class of schemes
Prismatic chromology
Regular rings
Cartier smoothness
Examples
Main Theorem
Italian Comparison Theorem
Related work