Mathematical Research Letters
Volume 20 (2013)
Lyubeznik numbers in mixed characteristic
Pages: 1125 – 1143
We define a family of invariants associated to any local ring whose residue field has prime characteristic; in particular, this includes those of mixed characteristic. These Lyubeznik numbers in mixed characteristic are defined via a surjection from an unramified regular local ring of mixed characteristic. As is true for the Lyubeznik numbers, the “highest-index” Lyubeznik number in mixed characteristic is a well-defined notion. These new invariants and the original Lyubeznik numbers coincide for certain local rings of equal characteristic $p \gt 0$; e.g., for Cohen-Macaulay rings and rings of dimension at most two. However, we provide an example where they differ.