A Relative Filtration Index and Fibers of Normal Primes in Extensions of Finite Type

For an extension R A of commutative Noetherian rings the behavior of the associated morphism of topological spaces Spec A Spec R is often measured by its behavior on each of its fibers. Specifically, one studies the 'splitting' (or 'branching') and the 'ramification' that occurs in each fiber. In the classical constructions of faithfully flat analytic extensions (e.g., completion or Henselization) of excellent local rings the splitting and ramification properties are fairly well understood; see EGA IV 6, 18.10], Nagata 13, Sect. 37] or Raynaud 15, Ch. IX]. The strongest results are usually achieved for fibers over a 'normal point' of Spec R, that is, over p Spec R such that R/p is a normal domain e.g., the property of a normal prime p in a local ring to be 'unibranched', i.e., the Henselization of R/p is a (normal) domain].