Cohomology of unbranched Riemann domains over $q$-complete spaces

Details Cohomology of unbranched Riemann domains over $q$-complete spaces Cohomology of unbranched Riemann domains over $q$-complete spaces

2011-12-29

arxiv.org/abs/1112.6292v1

Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 7, Number 4 (2011), pp. 449-456

Mathematics

Complex Variables

9 pages

Scientific paper

In this article, we show that if $\Pi: X\rightarrow Y$ is an unbranched Riemann domain over an $r$-complete complex space $Y$, then for any coherent analytic sheaf ${\mathcal{F}}$ on $X$ the cohomology group $H^{p}(X,{\mathcal{F}})$ vanishes for all $p\geq q+r-1.$ In particular, one gets a positive answer to a generalization of the local Stein problem and new vanishing theorems for the cohomology of locally $q$-complete open sets in $r$-complete spaces.

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