Big Cohen-Macaulay algebras and seeds

• Autores: Geoffrey D. Dietz
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 359, Nº 12, 2007, págs. 5959-5989
• Idioma: inglés
• DOI: 10.1090/s0002-9947-07-04252-3
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• Resumen

  • In this article, we delve into the properties possessed by algebras, which we have termed seeds, that map to big Cohen-Macaulay algebras. We will show that over a complete local domain of positive characteristic any two big Cohen-Macaulay algebras map to a common big Cohen-Macaulay algebra. We will also strengthen Hochster and Huneke's ``weakly functorial" existence result for big Cohen-Macaulay algebras by showing that the seed property is stable under base change between complete local domains of positive characteristic. We also show that every seed over a positive characteristic ring maps to a balanced big Cohen-Macaulay -algebra that is an absolutely integrally closed, -adically separated, quasilocal domain.