Vanishing of Ext, cluster tilting modules and finite global dimension of endomorphism rings

DOI10.1353/ajm.2013.0021zbMath1274.13031arXiv1005.5359OpenAlexW2117674547MaRDI QIDQ4917541

Hailong Dao, Craig Huneke

Publication date: 30 April 2013

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.5359

zbMATH Keywords

cluster tiltingAuslander correspondencenon-commutative crepant resolutionsExt vanishing

Mathematics Subject Classification ID

Representations of orders, lattices, algebras over commutative rings (16G30) Cohen-Macaulay modules in associative algebras (16G50) Homological functors on modules of commutative rings (Tor, Ext, etc.) (13D07)

Related Items (13)

Cluster tilting modules and noncommutative projective schemes ⋮ Tilting and cluster tilting for quotient singularities ⋮ On tensor products of matrix factorizations ⋮ \(G\)-groups of Cohen-Macaulay rings with \(n\)-cluster tilting objects ⋮ Refined multiplicative tensor product of matrix factorizations ⋮ Flops and clusters in the homological minimal model programme ⋮ A lockdown survey on cDV singularities ⋮ Singular derived categories of \(\mathbb{Q}\)-factorial terminalizations and maximal modification algebras ⋮ On the radical of endomorphism rings of local modules ⋮ Semi-steady non-commutative crepant resolutions via regular dimer models ⋮ Representation schemes and rigid maximal Cohen-Macaulay modules ⋮ Reduction of triangulated categories and maximal modification algebras for \(cA_n\) singularities ⋮ Noncommutative (crepant) desingularizations and the global spectrum of commutative rings

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