COMPLETIONS OF UFDs WITH SEMI-LOCAL FORMAL FIBERS
نویسنده
چکیده
Let T M be a complete local ring such that T/M = T . Given a finite set of incomparable nonmaximal prime ideals C of T , we provide necessary and sufficient conditions for T to be the completion of a local UFD A, whose generic formal fiber is semilocal with maximal ideals the elements of C. We also show that, given the T above, we can find necessary and sufficient conditions for T to be the completion of a UFD, whose formal fiber over a height one prime ideal is semilocal.
منابع مشابه
Chains of Unusual Excellent Local Rings
Let (T,M) be a complete local domain containing the integers. Let p1 ⊆ p2 ⊆ · · · ⊆ pn be a chain of nonmaximal prime ideals of T such that Tpn is a regular local ring. We construct a chain of excellent local domains An ⊆ An−1 ⊆ · · · ⊆ A1 such that for each 1 ≤ i ≤ n, the completion of Ai is T , the generic formal fiber of Ai is local with maximal ideal pi, and if I is a nonzero ideal of Ai th...
متن کاملTOP LOCAL COHOMOLOGY AND TOP FORMAL LOCAL COHOMOLOGY MODULES WITH SPECIFIED ATTACHED PRIMES
Let (R,m) be a Noetherian local ring, M be a finitely generated R-module of dimension n and a be an ideal of R. In this paper, generalizing the main results of Dibaei and Jafari [3] and Rezaei [8], we will show that if T is a subset of AsshR M, then there exists an ideal a of R such that AttR Hna (M)=T. As an application, we give some relationships between top local cohomology modules and top f...
متن کاملFormal Completions and Idempotent Completions of Triangulated Categories of Singularities
The main goal of this paper is to prove that the idempotent completions of the triangulated categories of singularities of two schemes are equivalent if the formal completions of these schemes along singularities are isomorphic. We also discuss Thomason theorem on dense subcategories and a relation to the negative K-theory.
متن کاملMultiple completions primed by occlusion patterns
There is a strong tendency to complete a partly occluded shape. Two types of pattern completion, global and local, are frequently reported. By means of the primed-matching paradigm, it has previously been shown that global completions are prevalent for stimuli in which regularity is abundantly present. In our study the primed-matching paradigm is applied to such stimuli in order to find out whe...
متن کاملMultiple completions primed by occlusion patterns.
There is a strong tendency to complete a partly occluded shape. Two types of pattern completion, global and local, are frequently reported. By means of the primed-matching paradigm, it has previously been shown that global completions are prevalent for stimuli in which regularity is abundantly present. In our study the primed-matching paradigm is applied to such stimuli in order to find out whe...
متن کامل