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- W3176087148 abstract "We study a pair of Calabi–Yau threefolds X and M, fibered in non-principally polarized Abelian surfaces and their duals, and an equivalence $$D^b(X) cong D^b(M)$$ , building on work of Gross, Popescu, Bak, and Schnell. Over the complex numbers, X is simply connected while $$pi _1(M) = (mathbf {Z}/3)^2$$ . In characteristic 3, we find that X and M have different Hodge numbers, which would be impossible in characteristic 0. In an appendix, we give a streamlined proof of Abuaf’s result that the ring $$mathrm{H}^{*}({mathscr {O}})$$ is a derived invariant of complex threefolds and fourfolds. A second appendix by Alexander Petrov gives a family of higher-dimensional examples to show that $$h^{0,3}$$ is not a derived invariant in any positive characteristic." @default.
- W3176087148 created "2021-07-05" @default.
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- W3176087148 date "2022-09-14" @default.
- W3176087148 modified "2023-10-15" @default.
- W3176087148 title "Hodge numbers are not derived invariants in positive characteristic" @default.
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- W3176087148 doi "https://doi.org/10.1007/s00208-022-02474-w" @default.
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