A04 New cohomology theories for arithmetic schemes

The goal of this project is to study cohomology theories for schemes in order to attack important open problems in arithmetic. Among these theories are topological periodic homology (TP), topological cyclic homology (TC), rational de Rham–Witt cohomology, prismatic cohomology, K-theory, L-Theory and leafwise cohomology of associated dynamical systems. We will prove structural results about those theories as well as make further calculations of specific cases.