Project A7: Generalized cohomology theories



Principal investigator

Participating scientist

Summary

Cohomology theories pervade large parts of algebraic and arithmetic geometry. The theory of motives for example is the theory of the target category of a universal cohomology theory for algebraic varieties.

In this project we will develop, study and apply old and new cohomology theories. These include foliation cohomology, algebraic and tale K-theory, (tale) homotopy theory and several version of cobordism theory: tale, algebraic, bivariant and enhanced with Hodge theory. Of particular interest are natural transformations between these theories and especially the Chern character and the closely related regulator map. Ideas from index theory are prominent. Among other applications, we are particularly interested in the study of algebraic cycles and L-functions using cohomological tools. Apart from algebraic methods we use a lot of analytic and topological techniques in the project. It is therefore on the borderline of the research areas A and B.

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