Resumen de 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 L, and a regular global section W ∈ (X,L). As an application, we establish the vanishing, in certain cases, of hRc (M, N), the higher Herbrand difference, and, ηRc (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/( f1,..., fc) has only isolated singularities, Q is a smooth k-algebra, k is a field of characteristic 0, the fi’s form a regular sequence, and c ≥ 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).
