Generic formal fibers and analytically ramified stable rings (Q2843354)

This paper explores the connection between the generic formal fiber of a local Noetherian domain \(A\) and the nature of the analytically ramified one-dimensional local rings which birationally dominate it. Specifically, it showed that the embedding dimension of birationally dominating analytically ramified stable local rings reflects the regularity, or lack thereof, of the generic formal fiber. One of the main result states that when \(A\) is an excellent local Noetherian domain of dimension \(d\), then the dimension of the generic formal fiber of \(A\) is \(d-1\) if and only if \(A\) is finitely dominated by an analytically ramified stable domain \(R\) of dimension \(d\).