We prove that any Fourier–Mukai partner of an abelian surface over an algebraically closed field of positive characteristic is isomorphic to a moduli space of Gieseker-stable sheaves. We apply this fact to show that the set of Fourier–Mukai partners of a canonical cover of a hyperelliptic or Enriques surface over an algebraically closed field of characteristic greater than three is trivial. These results extend earlier results of Bridgeland–Maciocia and Sosna to positive characteristic.

中文翻译：

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正特征中超椭圆曲面和恩里克斯曲面的典型覆盖的推导等价

我们证明了在具有正特征的代数闭域上的阿贝尔曲面的任何傅立叶-穆凯伙伴同构于 Gieseker 稳定滑轮的模空间。我们应用这个事实来表明，在特征大于 3 的代数闭域上的超椭圆或 Enriques 表面的典型覆盖的傅立叶-穆凯伙伴集是微不足道的。这些结果将 Bridgeland-Maciocia 和 Sosna 的早期结果扩展到积极特征。