2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64380We 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.The second part of the previous version is taken out and is moved to the new paper math.AG/0303189Commutative AlgebraAlgebraic Geometry13A35text