Kamil Rychlewicz, part1, `Zero schemes and equivariant cohomology theories' скачать в хорошем качестве

Kamil Rychlewicz, part1, `Zero schemes and equivariant cohomology theories'

Abstract: The classical Poincare-Hopf theorem shows how to read off the Euler characteristic from the local data on zeros of vector fields. Starting from the work of Carrell and Lieberman in the 70s, we know that in certain situations the whole cohomology ring can be deduced from the scheme structure on the zero scheme. I will report on the newest developments in the area regarding equivariant cohomology and K-theory. In particular, the cohomology ring of spherical varieties shows up as a ring of function on the zero schemes. I will also show how one can try to understand geometrically the cohomology rings of discriminant varieties.