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TitleA finiteness condition for algebras over coordinate rings of varieties
Author(s) Adam Hajduk, Stanisław Kasjan
TypeArticle in Journal
AbstractLet A be a finitely presented k [ X ] -algebra, where k [ X ] is the algebra of regular functions on a variety X defined over an algebraically closed field k . The following problem arises in the study of degenerations of algebras (Hajduk and Kasjan, in press [7]). Assume that the specialization of A at x has finite dimension over k for every x from a dense subset of X . Is there an open dense subset U of X such that the localization of A with respect to U is a finitely generated k [ U ] -module? We prove that this is the case if k has infinite transcendence degree over its prime subfield. We provide some applications to the concept of generalized CB-degenerations.
URL http://www.sciencedirect.com/science/article/pii/S0022404912002034
JournalJournal of Pure and Applied Algebra
Pages190 - 194
Translation No
Refereed No