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Stably reflexive modules and a lemma of Knudsen
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2014 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 397, 141-167 p.Article in journal (Refereed) Published
Abstract [en]

In his fundamental work on the stack (M) over bar (g,n) of stable n-pointed genus g curves, Finn F. Knudsen introduced the concept of a stably reflexive module in order to prove a key technical lemma. We propose an alternative definition and generalise the results in his appendix to [21]. Then we give a 'coordinate free' generalisation of his lemma, generalise a construction used in Knudsen's proof concerning versal families of pointed algebras, and show that Knudsen's stabilisation construction works for plane curve singularities. In addition we prove approximation theorems generalising Cohen-Macaulay approximation with stably reflexive modules in flat families. The generalisation is not covered (even in the closed fibres) by the Auslander-Buchweitz axioms.

Place, publisher, year, edition, pages
2014. Vol. 397, 141-167 p.
Keyword [en]
Stable curve, Cohen-Macaulay approximation, Versal deformation, Gorenstein dimension, Pointed singularity
National Category
URN: urn:nbn:se:kth:diva-134718DOI: 10.1016/j.jalgebra.2013.08.024ISI: 000326552000009ScopusID: 2-s2.0-84884371387OAI: diva2:668309

QC 20131129

Available from: 2013-11-29 Created: 2013-11-28 Last updated: 2013-11-29Bibliographically approved

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