Constructing perfect complexes with given intersection properties

In recent work, Roberts and Srinivas use geometric arguments to establish the existence of modules with unusual intersection properties. These modules are of finite length and finite projective dimension. They have Euler characteristic intersection pairings matching those of a cycle class in the kernel of the hyperplane section on a Chow group of a smooth projective scheme. More generally, a perfect complex, rather than an individual module of finite length and finite projective dimension, can be found with the correct Euler characteristic. This paper addresses how to construct perfect complexes with intersection properties prescribed by cycles in a Chow group.