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# Mathematical Research Letters

## Volume 20 (2013)

### Number 6

### Lyubeznik numbers in mixed characteristic

Pages: 1125 – 1143

DOI: http://dx.doi.org/10.4310/MRL.2013.v20.n6.a11

#### Authors

#### Abstract

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.