On the motivic filtration of TR - Faidon Andriopoulos

Ever since the work of Grothendieck, cohomology theories have proved to be indispensable tools in the study of algebraic geometry. They fit together under his visionary theory of motives, which in turn, is intricately related to the study of algebraic K-theory and its motivic filtration. In recent years, great new developments have occurred in the p-adic setting, with the development of prismatic cohomology and the study of the motivic filtration of topological Hochschild homology (THH) and its associated invariants. We plan to give a gentle introduction to some of these phenomena, by highlighting the role of the Witt vectors, working towards an understanding of the motivic filtration of topological restriction homology (TR).