Structure of Spectra of Precompletions
Commutative Algebra
2019-11-05 v1
Abstract
Let T be a complete local (Noetherian) ring and let A be a local subring of T such that the completion of A with respect to its maximal ideal is T. We investigate the possible structures of the partially ordered set Spec(A). Specifically, we explore the minimal prime ideals of A and their formal fibers, the maximal chains of prime ideals in A, and the number of prime ideals in A containing combinations of minimal prime ideals of A.
Keywords
Cite
@article{arxiv.1911.01394,
title = {Structure of Spectra of Precompletions},
author = {Erica Barrett and Emil Graf and S. Loepp and Kimball Strong and Sharon Zhang},
journal= {arXiv preprint arXiv:1911.01394},
year = {2019}
}
Comments
28 pages