Alina Bucur : Counting points on complete intersections over finite fields

Posted by Alina Carmen Cojocaru , part of the Number Theory Seminar.

At

Sept. 28, 2011, 10 a.m.

In

SEO 427

Abstract

I will give a quick overview of some new developments in counting points on curves over finite fields. Then we will concentrate on giving a probabilistic model for the number of rational points on a complete intersection of hypersufaces in projective n-space. A somewhat surprising corollary is that the number of rational points on a random smooth intersection of two curves in projective 3-space is strictly less than the number of points on the projective line. This is joint work with K. Kedlaya.