An Algebraic-Geometric Approach to NP Problems II

We explore in more detail how an actual probabilistic or quantum algorithm for NP-problems might be developed from the ideas in the previous paper. There we proved that there is an NP-complete problem which is equivalent to a system of a bounded number of diophantine equations of at most polynomial degree over a function K(t) where K can be a global field or its algebraic closure. This is equivalent to finding a section of a map from an algebraic variety to projective space of dimension 1. We suggested how this might be done for a curve. Here we propose that it could be done for a higher-dimensional algebraic variety by determining whether a generalized Brauer-Manin obstruction is trivial.