Claudia Miller,
The MacRae Invariant and the First Local Chern
Character
We discuss a paper by P. Roberts relating the McRae invariant (with the
definition suitably extended to bounded complexes of locally free sheaves)
to the first localized Chern character. The McRae invariant was introduced
to encapsulate the codimension one part of the support of a module of
finite projective dimension. It has been used by Foxby to show the
vanishing of some intersection multiplicities in case one module has
finite projective dimension, and by Roberts to show a vanishing theorem
over rings with singular locus of dimension one (via this relation to
localized Chern characters).