English

Gromov-Witten theory of schemes in mixed characteristic

Algebraic Geometry 2013-02-07 v2

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.

Keywords

Cite

@article{arxiv.1110.6395,
  title  = {Gromov-Witten theory of schemes in mixed characteristic},
  author = {Flavia Poma},
  journal= {arXiv preprint arXiv:1110.6395},
  year   = {2013}
}

Comments

This paper has been withdrawn by the author because the results have been enhanced and proved in the more general setting of tame Deligne-Mumford stacks in arXiv:1210.2269