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Noncommutative (crepant) desingularizations and the global spectrum of commutative rings. (English) Zbl 1327.14020
Let \(R\) be a commutative ring and \(M\) a finitely generated \(R\)–module, let \(A=\text{End}_R(M)\). If \(R\) is normal Gorenstein, \(M\) is reflexive and \(A\) is maximal Cohen–Macaulay with finite global dimension. \(A\) is a so–called crepant resolution of \(R\). Endomorphism rings of finite global dimension over commutative rings are studied. They occur as non-commutative crepant resolutions.

MSC:
14B05 Singularities in algebraic geometry
14A22 Noncommutative algebraic geometry
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
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