Compactification for essentially finite-type maps
Copyright policy )Compactification for essentially finite-type maps
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.
22 pages
Grothendieck duality, Mathematics(all), Essentially of finite type, localizing map, Schemes and morphisms, Birational map, 14A15 (Primary) 14E05 (Secondary), essentially of finite type, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), birational map, Mathematics - Algebraic Geometry, Nagata compactification, FOS: Mathematics, Localizing map, Algebraic Geometry (math.AG)
Grothendieck duality, Mathematics(all), Essentially of finite type, localizing map, Schemes and morphisms, Birational map, 14A15 (Primary) 14E05 (Secondary), essentially of finite type, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), birational map, Mathematics - Algebraic Geometry, Nagata compactification, FOS: Mathematics, Localizing map, Algebraic Geometry (math.AG)
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