Project C4: Milnor conjecture, Galois cohomology and algebraic cobordism

Summary:

The broader perspective is the development of cohomology theories in algebraic geometry. Central and classical topics in topology are singular cohomology, homotopy theory, and cobordism. Recent years brought successful definitions of corresponding theories in algebraic geometry known as motivic cohomology, <b>A</b>¹-homotopy and algebraic cobordism. A focal point in this development is the Milnor conjecture. It is on the one hand a basic statement about the Galois cohomology of fields and on the other hand involves much of the new techniques. The major goal of the project is the further development of the general framework and of applications to algebraic groups, Chow motives of classical varieties, birational invariants, K-theory and more.

Recent Preprints: