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dc.contributor.authorDao, Hailong
dc.contributor.authorLi, Jinjia
dc.contributor.authorMiller, Claudia
dc.identifier.citationDao, H.; Li, J.; Claudia, M.; On the (non)rigidity of the Frobenius endomorphism over Gorenstein rings. Algebra & Number Theory. Vol. 4 (2010), No. 8, 1039–1053. DOI: 10.2140/ant.2010.4.1039en_US
dc.description.abstractIt is well-known that for a large class of local rings of positive characteristic, including complete intersection rings, the Frobenius endomorphism can be used as a test for finite projective dimension. In this paper, we exploit this property to study the structure of such rings. One of our results states that the Picard group of the punctured spectrum of such a ring R cannot have p-torsion. When R is a local complete intersection, this recovers (with a purely local algebra proof) an analogous statement for complete intersections in projective spaces first given by Deligne in SGA and also a special case of a conjecture by Gabber. Our method also leads to many simply constructed examples where rigidity for the Frobenius endomorphism does not hold, even when the rings are Gorenstein with isolated singularity. This is in stark contrast to the situation for complete intersection rings. A related length criterion for modules of finite length and finite projective dimension is discussed towards the end.en_US
dc.publisherMathematical Sciences Publishers (MSP)en_US
dc.rightsCopyright ©2011 by Mathematical Sciences Publishers.en_US
dc.subjectFrobenius endomorphismen_US
dc.subjectPicard groupen_US
dc.subjectIsolated singularityen_US
dc.titleOn the (non)rigidity of the Frobenius endomorphism over Gorenstein ringsen_US
kusw.kuauthorDao, Hai Long
kusw.oanotesPer Sherpa Romeo 09/06/2022:

Algebra & Number Theory [Open panel below]Publication Information TitleAlgebra & Number Theory [English] ISSNs Print: 1937-0652 Electronic: 1944-7833 URL PublishersMathematical Sciences Publishers (MSP) [Commercial Publisher] [Open panel below]Publisher Policy Open Access pathways permitted by this journal's policy are listed below by article version. Click on a pathway for a more detailed view.

Published Version 6y Journal Website Embargo6 Years LocationJournal Website
kusw.oaversionScholarly/refereed, publisher versionen_US
kusw.oapolicyThis item meets KU Open Access policy criteria.en_US

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