Lyubeznik numbers in mixed characteristic

Abstract

This manuscript defines a new family of invariants, analogous to the Lyubeznik numbers, associated to any local ring whose residue field has prime characteristic. In particular, as their nomenclature suggests, these "Lyubeznik numbers in mixed characteristic" are defined for all local rings of mixed characteristic. Some properties similar to those in equal characteristic hold for these new invariants. Notably, the "highest" Lyubeznik number in mixed characteristic is a well-defined notion. Although the Lyubeznik numbers in mixed characteristic and their equal-characteristic counterparts are the same for certain local rings of equal characteristic p>0, we also provide an example where they differ.