ABHYANKAR 82nd BIRTHDAY CONFERENCE
SPEAKER: Sylvia Wiegand (Nebraska)
TITLE: Examples of integral domains inside power series rings
ABSTRACT: I will speak on joint work with Heinzer and Rotthaus on a technique
for constructing examples using power series. For R a Noetherian ring, the
constructed rings are either (1) an intersection $A=S\cap L$ of a power series
ring S over R with a field L between the field of fractions of R and the total
quotient ring of S, or (2) a certain nested union B of polynomial rings
$B_i=R[\tau_{i1},\dots,\tau_{In}]$ over R, where for each $i$ the $\tau_{ij}$ are
elements of S that are algebraically independent over R. Certain flatness
conditions imply that the two rings A and B are equal, or that they are both
Noetherian and equal. We describe specific examples as time permits.