Summary: SOME APPLICATIONS OF POSITIVE
CHARACTERISTIC TECHNIQUES TO VANISHING
THEOREMS
DONU ARAPURA
To Joe Lipman
These are notes to my talk at Lipman's birthday conference. Some
details have appeared in [A1, A2]. The rest hopefully will someday.
1. Differential Forms
Let X be a smooth complete variety over C. Then
as a consequence of Hodge theory + GAGA:
Hi
(Xan
, C) = Hi
(X, ·
X) =
a+b=i
Hb
(X, a
X)
If X is complete but singular, then both these iso-

Source: Arapura, Donu - Department of Mathematics, Purdue University

Collections: Mathematics