Dori Bejleri, April 21, 2023
Title: Height moduli on cyclotomic stacks
Abstract: Heights on stacks were recently introduced by Ellenberg, Satriano and Zureick-Brown as a tool to unify and generalize various results and conjectures about counting arithmetic objects. Cyclotomic stacks are a particularly well behaved class of stacks which share many similarities with projective varieties. In this talk I will present a geometric approach to heights on cyclotomic stacks and a construction of moduli spaces of points of fixed height in the function field case. This allows us to lift counts of arithmetic objects to the Grothendieck ring of varieties and use tools from algebraic geometry and topology to count rational points. I will explain some applications to counting elliptic curves over function fields and some general conjectures. This is based on joint work with Park and Satriano.