IJPAM: Volume 43, No. 3 (2008)

COHOMOLOGICAL DIMENSION OF
QUASI-AFFINE VARIETIES

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Let $Y$ be an affine and smooth $n$-dimensional algebraic scheme of finite type over a field $K$ and $X$ a non-empty open subset of $Y$. Here we prove that $cd(X)$ is the first integer $t$ such that $h^i(X,\mathcal {O}_X)=0$ for all $i > t$.

Received: December 26, 2007

AMS Subject Classification: 14F17

Key Words and Phrases: cohomological dimension, quasi-affine scheme

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 43
Issue: 3