  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.
