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Liftable derivations of generically separably algebraic morphisms of schemes
University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik. (Matematik)
2009 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 361, no 1, 495-523 p.Article in journal (Refereed) Published
Abstract [en]

We consider dominant, generically algebraic (e. g. generically finite), and tamely ramified (if the characteristic is positive) morphisms pi : X/S -> Y/S of S-schemes, where Y, S are Noetherian and integral and X is a Krull scheme (e. g. normal Noetherian), and study the sheaf of tangent vector fields on Y that lift to tangent vector fields on X. We give an easily computable description of these vector fields using valuations along the critical locus. We apply this to answer the question when the liftable derivations can be defined by a tangency condition along the discriminant. In particular, if p is a blow-up of a coherent ideal I, we show that tangent vector fields that preserve the Ratliff-Rush ideal (equals [I(n+1) : I(n)] for high n) associated to I are liftable, and that all liftable tangent vector fields preserve the integral closure of I. We also generalise in positive characteristic Seidenberg's theorem that all tangent vector fields can be lifted to the normalisation, assuming tame ramification.

Place, publisher, year, edition, pages
2009. Vol. 361, no 1, 495-523 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:hig:diva-1672DOI: 10.1090/S0002-9947-08-04534-0ISI: 000259551400020Scopus ID: 2-s2.0-77950472639OAI: oai:DiVA.org:hig-1672DiVA: diva2:118334
Available from: 2008-05-09 Created: 2008-05-09 Last updated: 2016-10-27Bibliographically approved

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard-cite-them-right
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • sv-SE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • de-DE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf