dc.creator | Narváez Macarro, Luis | es |
dc.date.accessioned | 2016-06-29T12:15:51Z | |
dc.date.available | 2016-06-29T12:15:51Z | |
dc.date.issued | 2012-03-20 | |
dc.identifier.citation | Narváez Macarro, L. (2012). On the modules of m-integrable derivations in non-zero characteristic. Advances in Mathematics, 229 (5), 2712-2740. | |
dc.identifier.issn | 0001-8708 | es |
dc.identifier.issn | 1090-2082 | es |
dc.identifier.uri | http://hdl.handle.net/11441/42934 | |
dc.description.abstract | 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 locally mintegrable
form a quasi-coherent submodule Ider S(OX; m) ⊂ Der S(OX)
such that, for any affine open sets U = Spec A ⊂ X and V = Spec k ⊂
S, with f(U) ⊂ V , we have Γ(U,Ider S(OX; m)) = Iderk(A; m) and
Ider S(OX; m)p = IderOS,f(p)
(OX,p; m) for each p ∈ X. We also give,
for each positive integer m, an algorithm to decide whether all derivations
are m-integrable or not. | es |
dc.description.sponsorship | Ministerio de Educación y Ciencia | es |
dc.description.sponsorship | Fondo Europeo de Desarrollo Regional | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | Elsevier | es |
dc.relation.ispartof | Advances in Mathematics, 229 (5), 2712-2740. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Derivation | es |
dc.subject | Integrable derivation | es |
dc.subject | Hasse–Schmidt derivation | es |
dc.subject | Differential operator | es |
dc.title | On the modules of m-integrable derivations in non-zero characteristic | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/submittedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de álgebra | es |
dc.relation.projectID | MTM2007-66929 | es |
dc.relation.projectID | MTM2010-19298 | es |
dc.relation.publisherversion | http://dx.doi.org/10.1016/j.aim.2012.01.015 | es |
dc.identifier.doi | 10.1016/j.aim.2012.01.015 | es |
dc.contributor.group | Universidad de Sevilla. FQM218: Geometria Algebraica, Sistemas Diferenciales y Singularidades | es |
idus.format.extent | 29 p. | es |
dc.journaltitle | Advances in Mathematics | es |
dc.journaltitle | Advances in Mathematics | es |
dc.publication.volumen | 229 | es |
dc.publication.volumen | 229 | es |
dc.publication.issue | 5 | es |
dc.publication.issue | 5 | es |
dc.publication.initialPage | 2712 | es |
dc.publication.initialPage | 2712 | es |
dc.publication.endPage | 2740 | es |
dc.publication.endPage | 2740 | es |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/42934 | |
dc.contributor.funder | Ministerio de Educación y Ciencia (MEC). España | |
dc.contributor.funder | European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) | |