Searcharxiv⌕ Search

arXiv subjects

Graham Leuschke

Publications and source records attributed to Graham Leuschke.

2 recordsLinked to original sources
arXiv2003

On a conjecture of Auslander and Reiten

In studying Nakayama's 1958 conjecture on rings of infinite dominant dimension, Auslander and Reiten proposed the following generalization: Let Lambda be an Artin algebra and M a Lambda-generator such that Ext^i_Lambda(M,M)=0 for all i \geq 1; then M is projective. This conjecture makes sense for any ring. We establish Auslander and Reiten's conjecture for excellent Cohen--Macaulay normal domains containing the rational numbers, and slightly more generally.

math.AC↗
arXiv2002

Local rings of countable Cohen--Macaulay type

We prove (the excellent case of) Schreyer's conjecture that a local ring with countable Cohen--Macaulay type has at most a one-dimensional singular locus. Furthermore we prove that the localization of a Cohen-Macaulay local ring of countable CM type is again of countable CM type.

math.AC↗