Big Cohen-Macaulay Algebras and Seeds

Details Big Cohen-Macaulay Algebras and Seeds Big Cohen-Macaulay Algebras and Seeds

2005-08-18

arxiv.org/abs/math/0508358v2

Trans. of the Amer. Math. Soc., 359 (2007), No. 12, 5959--5989

Mathematics

Commutative Algebra

31 pages, typos corrected, Journal-ref added

Scientific paper

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 local ring (R,m) maps to a big Cohen-Macaulay R-algebra that is an absolutely integrally closed, m-adically separated, quasilocal domain.

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