Generic fiber of power series ring extensions

TL;DR

This paper investigates the structure of power series ring extensions over Noetherian domains, showing that the generic fiber dimension exceeds that of the base domain modulo a nonzero nonunit.

Contribution

It establishes a new lower bound on the generic fiber dimension for specific power series ring extensions over Noetherian domains.

Findings

The generic fiber of D[1/d][[z]] over D[[z]] has dimension greater than dim(D/dD).

Provides insight into the structure of power series ring extensions.

Advances understanding of fiber dimensions in algebraic geometry.

Abstract

Let D be a Noetherian domain containing a field, d a nonzero nonunit of D and z an indeterminate over D. We prove that the generic fiber of D[1/d][[z]] over D[[z]] has dimension greater than the dimension of D/dD.