Semilocal Generic Formal Fibers

Let T be a complete local ring and C a finite set of incomparable prime ideals of T. We find necessary and sufficient conditions for T to be the completion of an integral domain whose generic formal fiber is semilocal with maximal ideals the elements of C. In addition, if char T = 0, we give necessary and sufficient conditions for T to be the completion of an excellent integral domain whose generic formal fiber is semilocal with maximal ideals the elements of C.Comment: 15 page

Characterization of completions of excellent domains of characteristic zero

AbstractWe show that a complete local ring T containing the integers is the completion of a local excellent integral domain if and only if it is reduced, equidimensional, and no integer of T is a zero divisor

Gluing Associated Prime Ideals of Small Height

Let $B$ be a local (Noetherian) ring and suppose that $B$ has $n$ associated prime ideals where $n \geq 2$. We identify sufficient conditions for there to exist a local (Noetherian) subring $S$ of $B$ such that $S$ and $B$ have the same completion and $S$ has exactly $n - 1$ associated prime ideals. We include applications and consequences of this result.Comment: 14 page