`Vanishing of the higher direct images of the structure sheaf'

by Prof. Kay Ruelling (Freie University, Germany)

Tuesday 21 Oct 2014, 08:00 → 09:00 Asia/Kolkata

AG-77 (Mumbai)

Let $f: X \dashrightarrow Y$ be a birational and projective
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-R\"ulling in 2011. In this talk I will explain the
proof in the general case. This is joint work with Andre Chatzistamatiou.