Cohomological dimension, Lyubeznik numbers, and connectedness properties in mixed characteristic
arXiv:1609.05846
Abstract
We establish a "second vanishing theorem" for local cohomology modules over regular rings of unramified mixed characteristic, which relates the connectedness of the spectrum of a ring with the vanishing of local cohomology. Applying this, and new results on the mixed characteristic Lyubeznik numbers, we further study connectedness properties of the spectra of a certain class of rings.
21 pages, comments welcome!