Let be a complete local (Noetherian) ring, and let be a local subring of such that the completion of with respect to its maximal ideal is . We investigate the possible structures of the partially ordered set . Specifically, we explore the minimal prime ideals of and their formal fibers, the maximal chains of prime ideals in , and the number of prime ideals in containing combinations of minimal prime ideals of .
"Structure of spectra of precompletions." Rocky Mountain J. Math. 50 (6) 1965 - 1988, December 2020. https://doi.org/10.1216/rmj.2020.50.1965