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On the modules of m-integrable derivations in non-zero characteristic

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Autor: Narváez Macarro, Luis
Departamento: Universidad de Sevilla. Departamento de álgebra
Fecha: 2012-03-20
Publicado en: Advances in Mathematics, 229 (5), 2712-2740.
Tipo de documento: Artículo
Resumen: Let k be a commutative ring and A a commutative k-algebra. Given a positive integer m, or m = ∞, we say that a k-linear derivation δ of A is m-integrable if it extends up to a Hasse–Schmidt derivation D = (Id, D1 = δ, D2, . . . , Dm) of A over k of length m. This condition is automatically satisfied for any m under one of the following orthogonal hypotheses: (1) k contains the rational numbers and A is arbitrary, since we can take Di = δ i i! ; (2) k is arbitrary and A is a smooth k-algebra. The set of m-integrable derivations of A over k is an A-module which will be denoted by Iderk(A; m). In this paper we prove that, if A is a finitely presented k-algebra and m is a positive integer, then a k-linear derivation δ of A is m-integrable if and only if the induced derivation δp : Ap → Ap is m-integrable for each prime ideal p ⊂ A. In particular, for any locally finitely presented morphism of schemes f : X → S and any positive integer m, the S-derivations of X which are l...
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Cita: Narváez Macarro, L. (2012). On the modules of m-integrable derivations in non-zero characteristic. Advances in Mathematics, 229 (5), 2712-2740.
Tamaño: 357.7Kb
Formato: PDF

URI: http://hdl.handle.net/11441/42934

DOI: http://dx.doi.org/10.1016/j.aim.2012.01.015

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