Canonical Big Cohen-Macaulay algebras and rational singularities

Details Canonical Big Cohen-Macaulay algebras and rational singularities Canonical Big Cohen-Macaulay algebras and rational singularities

2002-06-24

arxiv.org/abs/math/0206250v2

Illinois J. Math. 48 (2004), 131-150

Mathematics

Commutative Algebra

The second part of the previous version is taken out and is moved to the new paper math.AG/0303189

Scientific paper

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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