Beyond the current motivic cohomology theory
Cohomology is originally part of geometry and the theory of spaces, used to capture and linearise subtle geometric and topological information. It has been extended in many ways to algebraic geometry and number theory, where it can now encode arithmetic information relevant to numerous important unsolved problems. A particular, and in some sense universal, cohomology theory is the geometric motivic cohomology developed from the 1980s to the 2000s. The EU-funded MoCoS project is developing an extension of this motivic cohomology to the arithmetic, and even singular, context. It relies on recent breakthroughs in homotopy theory and arithmetic geometry, such as topological cyclic homology and perfectoids.
Fields of science
Funding SchemeERC-COG - Consolidator Grant