Lifting automorphisms on Abelian varieties as derived autoequivalences

Abstract

We show that on an Abelian variety over an algebraically closed field of positive characteristic, the obstruction to lifting an automorphism to a field of characteristic zero as a morphism vanishes if and only if it vanishes for lifting it as a derived autoequivalence. We also compare the deformation space of these two types of deformations.

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Acknowledgements

I would like to thank Piotr Achinger, Daniel Huybrechts, Katrina Honigs, Marcin Lara, and Maciek Zdanowicz for the mathematical discussions, Tamas Hausel for hosting me in his research group at IST Austria, and the referees for their valuable suggestions. This research has received funding from the European Union’s Horizon 2020 research and innovation programme under Marie Sklodowska-Curie Grant Agreement No. 754411.

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Correspondence to Tanya Kaushal Srivastava.

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Srivastava, T.K. Lifting automorphisms on Abelian varieties as derived autoequivalences. Arch. Math. (2021). https://doi.org/10.1007/s00013-020-01564-y

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Mathematics Subject Classification

  • 14F05
  • 14J50
  • 14G17
  • 11G10
  • 14D15
  • 14K99

Keywords

  • Abelian varieties
  • Automorphisms
  • Positive characteristic
  • Derived autoequivalences
  • Lifting to characteristic zero