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Purity of Branch and Critical locus
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences. (Matematik)
2013 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 379, 156-178 p.Article in journal (Refereed) Published
Abstract [en]

To a dominant morphism $X/S \to Y/S$ of N\oe therian integral $S$-schemes one has the inclusion $C_{X/Y}\subset B_{X/Y}$ of the critical locus in the branch locus of $X/Y$. Starting from the notion of locally complete intersection morphisms, we give conditions on the modules of relative differentials $\Omega_{X/Y}$, $\Omega_{X/S}$, and $\Omega_{Y/S}$ that imply bounds on the codimensions of $ C_{X/Y}$ and $ B_{X/Y}$. These bounds generalise to a wider class of morphisms the classical purity results for finite morphisms by Zariski-Nagata-Auslander, and Faltings and Grothendieck, and van der Waerden's purity for birational morphisms.

Place, publisher, year, edition, pages
2013. Vol. 379, 156-178 p.
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:hig:diva-13720DOI: 10.1016/j.jalgebra.2013.01.006ISI: 000319169800009Scopus ID: 2-s2.0-84873153095OAI: oai:DiVA.org:hig-13720DiVA: diva2:600947
Available from: 2013-01-28 Created: 2013-01-28 Last updated: 2014-01-28Bibliographically approved

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