Colloquium: Tuesday, May 22, 2 pm. Speaker: Alexei Entin (Tel Aviv). Title: “Monodromy of hyperplane sections of curves and decomposition statistics over finite fields”.
For a projective curve C defined over F_q we study the statistics of the F_q-structure of a section of C by a random hyperplane defined over F_q in the $q\to\infty$ limit. We obtain a very general equidistribution result for this problem. We deduce many old and new results about decomposition statistics over finite fields in this limit. Our main tool will be the calculation of the monodromy of transversal hyperplane sections of a projective curve.