Use this resource - and many more! - in your textbook!
AcademicPub holds over eight million pieces of educational content for you to mix-and-match your way.
Counting points on varieties over finite fields related to a conjecture of Kontsevich
By: John Stembridge;
1998 / Springer Science+Business Media / 0218-0006
We describe a characteristic-free algorithm for “reducing” an algebraic variety defined by the vanishing of a set of integer polynomials. In very special cases, the algorithm can be used to decide whether the number of points on a variety, as the ground field varies over finite fields, is a polynomial function of the size of the field. The algorithm is then used to investigate a conjecture of Kontsevich regarding the number of points on a variety associated with the set of spanning trees of any graph. We also prove several theorems describing properties of a (hypothetical) minimal counterexample to the conjecture, and produce counterexamples to some related conjectures.