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arXiv · 1911.01394

Structure of Spectra of Precompletions

Erica Barrett·Emil Graf·S. Loepp·Kimball Strong·Sharon Zhang
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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.

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Erica Barrett, Emil Graf, S. Loepp, Kimball Strong, Sharon Zhang. 2019-11-04. Structure of Spectra of Precompletions. https://arxiv.org/abs/1911.01394

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