Compactification for essentially finite-type maps

Details Compactification for essentially finite-type maps Compactification for essentially finite-type maps

2008-09-08

arxiv.org/abs/0809.1201v1

Mathematics

Algebraic Geometry

22 pages

Scientific paper

We show that any separated essentially finite-type map $f$ of noetherian schemes globally factors as $f = hi$ where $i$ is an injective localization map and $h$ a separated finite-type map. In particular, via Nagata's compactification theorem, $h$ can be chosen to be proper. We apply these results to Grothendieck duality. We also obtain other factorization results and provide essentialized versions of many general results such as Zariski's Main Theorem, Chow's Lemma, and blow-up descriptions of birational maps.

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