Abstract
This chapter describes the dimension of formal fibers of a local ring. If (A, m) is a noetherian local ring and A is its m-adic completion. The fibers of the morphism Spec(Â) → Spec(A) are the formal fibers of A. As  has very good properties and as  is flat over A, A has a good property if the formal fibers have related good properties. This is the philosophy of Grothendieck's theory of excellent rings. The fiber over the generic point (0) of Spec(A) is called the generic fiber.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Algebraic Geometry and Commutative Algebra in Honor of Masayoshi Nagata
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
