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Stably reflexive modules and a lemma of Knudsen
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
2014 (engelsk)Inngår i: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 397, s. 141-167Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
2014. Vol. 397, s. 141-167
Emneord [en]
Stable curve, Cohen-Macaulay approximation, Versal deformation, Gorenstein dimension, Pointed singularity
HSV kategori
Identifikatorer
URN: urn:nbn:se:kth:diva-134718DOI: 10.1016/j.jalgebra.2013.08.024ISI: 000326552000009Scopus ID: 2-s2.0-84884371387OAI: oai:DiVA.org:kth-134718DiVA, id: diva2:668309
Merknad

QC 20131129

Tilgjengelig fra: 2013-11-29 Laget: 2013-11-28 Sist oppdatert: 2017-12-06bibliografisk kontrollert

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Totalt: 31 treff
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  • sv-SE
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