Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

According to the Grothendieck idea every algebraic variety is built in some sense from indecomposable pieces. These pieces are called motives.When a cohomology theory is applied to a variety (i.e. a certain type of functor from varieties to an abelian category), then the decomposition is visible as a decomposition into a direct sum. We will discuss an example of such decomposition coming from an action of C^* (for complex varieties).We confront this decomposition with the localization theorem in equivariant cohomology.