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Pure and Applied Mathematics Quarterly
Volume 19 (2023)
Special Issue in honor of Don Zagier
Guest editors: Benedict H. Gross, Ken Ono, and Fernando Rodriguez Villegas
On $p$-integrality of instanton numbers
Pages: 7 – 44
We show integrality of instanton numbers in several key examples of mirror symmetry. Our methods are essentially elementary, they are based on our previous work in the series of papers called Dwork crystals I, II and III.
instanton number, Picard–Fuchs equation, Frobenius structure, $p$-adic cohomology
2010 Mathematics Subject Classification
Primary 12H25, 14N35. Secondary 14F30.
The work of Frits Beukers was supported by the Netherlands Organisation for Scientific Research (NWO), grant TOP1EW.15.313.
The work of Masha Vlasenko was supported by the National Science Centre of Poland (NCN), grant UMO-2020/39/B/ST1/00940.
Received 21 September 2021
Accepted 13 May 2022
Published 3 April 2023