Let R be a commutative, noetherian, local ring. Topological Q-vector spaces modelled on full subcategories of the derived category of R are constructed in order to study intersection multiplicities.
Let x~ be the image of X~ in R. The main object of this paper is to study modules of finite length and finite projective dimension over R. One consequence of our study will be counterexamples to several conjectures concerning the behavior of intersection multiplicities for modules of finite projective dimension. Let "/" denote length. If S is a Noetherian ring, M, N are finitely generated S-modules, l(M| ) is finite, and d=pdsM<~, we may define, following Serre IS] d Zs(M, N)= z(M, N) = ~ ( 1)'/(TorS(M, N)).
In the conventional approach to quantum mechanics, indeterminism is an axiom and nonlocality is a theorem. We consider inverting the logical order, making nonlocality an axiom and indeterminism a theorem. Nonlocal “superquantum” correlations, preserving relativistic causality, can violate the CHSH inequality more strongly than any quantum correlations.