Height moduli on algebraic stacks and counting families of varieties

Jun-Yong Park, University of Melbourne

I will begin by reviewing a classical algorithm of Tate with some explicit polynomial calculations. Combining this with twisted stable maps theory leads us to the height moduli of rational points of fixed stacky height on the fine modular curve Mbar_{1,1} over global function fields. We will then compute arithmetic invariants of elliptic surfaces moduli via topological methods and give applications to counting elliptic curves over Fq(t).

MC 5417