Canonical Big Cohen-Macaulay algebras and rational singularities
classification
🧮 math.AC
math.AG
keywords
canonicalcharacteristiccohen-macaulayrationalsingularitiesabsolutealgebraalgebras
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We give a canonical construction of a balanced big Cohen-Macaulay algebra for a domain of finite type over $\mathbb C$ by taking ultraproducts of absolute integral closures in positive characteristic. This yields a new tight closure characterization of rational singularities in characteristic zero.
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