Gromov-Witten theory of schemes in mixed characteristic

Details Gromov-Witten theory of schemes in mixed characteristic Gromov-Witten theory of schemes in mixed characteristic

2011-10-28

arxiv.org/abs/1110.6395v1

Mathematics

Algebraic Geometry

42 pages, 6 sections, 2 appendices. Preliminary version, comments welcome

Scientific paper

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.

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