Abstract

A hundred years ago Jacob Nielsen proposed a lower bound on the number of fixed points of a self-map, utilizing the action on the fundamental group. The natural bookkeeping device is the Reidemeister trace, a linear combination of twisted conjugacy classes. I will review the classical theory and propose an analogue for varieties over finite fields, in the spirit of the rationality part of the Weil conjectures, where the self-map is replaced by the Frobenius automorphism. The resulting conjecture can be checked in non-trivial examples.