Counting Points on Varieties over Finite Fields Related to a Conjecture of Kontsevich *

@inproceedings{Stembridge1998CountingPO,
  title={Counting Points on Varieties over Finite Fields Related to a Conjecture of Kontsevich *},
  author={John R. Stembridge},
  year={1998}
}
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… CONTINUE READING
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