Abstract Kay Rülling

Title: Higher direct images of the structure sheaf under a birational morphism between regular schemes

Abstract: Let f: X---> Y be a projective and birational morphism between excellent and regular schemes. Then the higher direct images of the structure sheaf of X under f, R^i f_* O_X, vanish for all positive integers i. In case X and Y are smooth schemes over a field of characteristic zero, this vanishing was proved by Hironaka as a corollary of his proof of the existence of resolutions of singularities. In case X and Y are smooth over a field of positive characteristic the statement was proved by Chatzistamatiou-Rülling in 2011. In this talk I will explain the proof in the general case. This is joint work with Andre Chatzistamatiou.