Abstract

Let R be the quotient of a local domain (Q,n) by a proper ideal minimally generated by f₁,…,f_c. Assume Q ∕ n is algebraically closed, and let M and N be finitely generated R-modules. We show there is an algebraic set in c-dimensional afine space, called the support set of the pair (M,N), which describes those hypersurfaces h in (f₁,…,f_c) − n(f₁,…,f_c) over which there are infinitely many nonzero Ext_{Q ∕ (h)}ⁱ(M,N). This generalizes to arbitrary quotients of regular local rings the notion of support variety for modules over complete intersections.

Authors