Motivic Integral p-adic Cohmologies

Voevodsky’s theory of motives and its subsequent developments have been crucial in proving long-standing conjectures about étale cohomology and K-theory, but the assumption of A1-invariance forces to leave out many interesting objects, especially integral p-adic theories like (Witt-) differential forms, p-adic étale cohomology and (Topological) Hochschild and cyclic homology. I will present the construction and properties of various motivic categories based on logarithmic schemes, applications to the aforementioned cohomology theories and conjectures. This is a joint project with F. Binda, T. Lundemo, D. Park and P. A. Østvær.