Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Liftable derivations for generically separably algebraic morphisms of schemes

Author: Rolf Källström
Journal: Trans. Amer. Math. Soc. 361 (2009), 495-523
MSC (2000): Primary 14E22, 13N15; Secondary 14Axx, 13B22, 16W60
Published electronically: June 26, 2008
MathSciNet review: 2439414
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider dominant, generically algebraic (e.g. generically finite), and tamely ramified (if the characteristic is positive) morphisms $ \pi : X/S \to Y/S$ of $ S$-schemes, where $ Y,S$ are Nœtherian and integral and $ X$ is a Krull scheme (e.g. normal Nœtherian), 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 $ \pi$ 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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 14E22, 13N15, 14Axx, 13B22, 16W60

Retrieve articles in all journals with MSC (2000): 14E22, 13N15, 14Axx, 13B22, 16W60

Additional Information

Rolf Källström
Affiliation: Department of Mathematics, University of Gävle, 801 76 Gävle, Sweden

Received by editor(s): November 22, 2006
Received by editor(s) in revised form: April 13, 2007
Published electronically: June 26, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.