Bielliptic and quasi-bielliptic surfaces form one of the four classes of minimal smooth projective surfaces of Kodaira dimension $0$. In this article, we determine the automorphism schemes of these surfaces over algebraically closed fields of arbitrary characteristic, generalizing work of Bennett and Miranda over the complex numbers; we also find some cases that are missing from the classification of automorphism groups of bielliptic surfaces in characteristic $0$.

Comment: 21 pages, final version

• 14G17 - Positive characteristic ground fields in algebraic geometry
• 14J27 - Elliptic surfaces, elliptic or Calabi-Yau fibrations
• 14J50 - Automorphisms of surfaces and higher-dimensional varieties
• 14L15 - Group schemes

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