2016/08/29 by Geoffrey D. Dietz, Dietz, Geoffrey D., Rebecca R. G +1
Mathematics · #03C20 (Secondary) #13C14 (Primary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1608.08193
openalex publication_date 2016/08/29 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Let R be a commutative, local, Noetherian ring. In a past article, the\nfirst author developed a theory of R-algebras, termed seeds, that can be\nmapped to balanced big Cohen-Macaulay R-algebras. In prime characteristic\np, seeds can be characterized based on the existence of certain\ncolon-killers, integral extensions of seeds are seeds, tensor products of seeds\nare seeds, and the seed property is stable under base change between complete,\nlocal domains. As a result, there exist directed systems of big Cohen-Macaulay\nalgebras over complete, local domains. In this work, we will show that these\nproperties can be extended to analogous results in equal characteristic zero.\nThe primary tool for the extension will be the notion of ultraproducts for\ncommutative rings as developed by Schoutens and Aschenbrenner.\n