Non-noetherian krull domains issued from symbolic blow-up and rees algebras

Abstract

Since Seidenberg's work on the dimension of polynomial rings in 1952, we know that Noetherian domains have the Krull dimension coincide with the valuative dimension (i.e., are Jaffard domains in non-Noetherian jargon). It is still an open problem to know whether this holds for arbitrary finite-dimensional Krull domains. However, non-Noetherian finite-dimensional Krull domains are rare in the literature and all happen to be Jaffard. Some of them arise as symbolic blow-up algebras or symbolic Rees algebras. Our purpose in this MS thesis is to have a close look at various works on this subject, towards a better understanding of non-Noetherian finite-dimensional Krull structures; particularly, those issued from blow-up and Rees algebras.