An explicit and uniform Manin-Mumford-type result for function fields

Robert Wilms

Published 2021-01-27Version 1

We prove that any smooth projective geometrically connected non-isotrivial curve of genus $g\ge 2$ over a function field of any characteristic has at most $112g^2+240g+380$ torsion points for any Abel-Jacobi embedding of the curve into its Jacobian. The proof basically uses Zhang's admissible pairing on curves, the arithmetic Hodge index theorem for function fields and the metrized graph analogue of Elkie's lower bound for the Green function.