Chern characters for twisted matrix factorizations and the vanishing of the higher Herbrand difference.

We develop a theory of 'ad hoc' Chern characters for twisted matrix factorizations associated to a scheme X, a line bundle $$\mathcal {L}$$ , and a regular global section $$W \in \Gamma (X, \mathcal {L})$$ . As an application, we establish the vanishing, in certain cases, of $$h_c^R(M,N)$$ , the higher Herbrand difference, and, $$\eta _c^R(M,N)$$ , the higher codimensional analogue of Hochster's theta pairing, where R is a complete intersection of codimension c with isolated singularities and M and N are finitely generated R-modules. Specifically, we prove such vanishing if $$R = Q/(f_1, \dots , f_c)$$ has only isolated singularities, Q is a smooth k-algebra, k is a field of characteristic 0, the $$f_i$$ 's form a regular sequence, and $$c \ge 2$$ . Such vanishing was previously established in the general characteristic, but graded, setting in Moore et al. (Math Z 273(3-4):907-920, 2013). [ABSTRACT FROM AUTHOR]