Gromov-Witten theory of schemes in mixed characteristic

Abstract

We define Gromov-Witten classes and invariants of smooth projective schemes of finite presentation over a Dedekind domain. We prove that they are deformation invariants and verify the fundamental axioms. For a smooth projective scheme over a Dedekind domain, we prove that the invariants of fibers in different characteristics are the same. We show that genus zero Gromov-Witten invariants define a potential which satisfies the WDVV equation and we deduce from this a reconstruction theorem for genus zero Gromov-Witten invariants in arbitrary characteristic.

This paper has been withdrawn by the author because the results have been enhanced and proved in the more general setting of tame Deligne-Mumford stacks in arXiv:1210.2269