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What is an example of an abelian variety over a finite field $\mathbb{F}_p$ which doesn't lift to $\mathbb{Z}_p$? This question seems to hint that they should exist, but no example is given.

Note that I want to consider just abelian varieties and not abelian varieties equipped with a polarisation.

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    $\begingroup$ Oort gives examples of abelian varieties over a field $k$ of characteristic $p$ that don't lift to $W(k)$. Oort, Frans. Lifting algebraic curves, abelian varieties, and their endomorphisms to characteristic zero. Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), 165--195, Proc. Sympos. Pure Math., 46, Part 2, Amer. Math. Soc., Providence, RI, 1987. $\endgroup$
    – anon
    Commented Sep 13, 2023 at 17:16
  • $\begingroup$ @anon: Thanks for the comments. I have looked at this paper. I can't find a statement in this paper which addresses my question. Can you please be more precise? Section 12 comes closest, but I can't see any finite fields in this section. $\endgroup$
    – Daniel Loughran
    Commented Sep 13, 2023 at 20:35
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    $\begingroup$ @DanielLoughran Oort doesn't construct examples of finite fields, only over some fields of char $p>0$. This is also what anon writes. $\endgroup$
    – Ariyan Javanpeykar
    Commented Sep 14, 2023 at 3:18

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