Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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WEIGHTED PROJECTIVE LINES WITH WEIGHT PERMUTATION

  • Han, Lina (Yau Mathematical Sciences Center Tsinghua University) ;
  • Wang, Xintian (College of Science China University of Mining and Technology (Beijing))
  • Received : 2020.01.28
  • Accepted : 2020.08.31
  • Published : 2021.01.01
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Abstract

Let �� be a weighted projective line defined over the algebraic closure $k={\bar{\mathbb{F}}}_q$ of the finite field ��q and σ be a weight permutation of ��. By folding the category coh-�� of coherent sheaves on �� in terms of the Frobenius twist functor induced by σ, we obtain an ��q-category, denoted by coh-(��, σ; q). We then prove that coh-(��, σ; q) is derived equivalent to the valued canonical algebra associated with (��, σ).

Keywords

Acknowledgement

The authors are very grateful to Professor Bangming Deng for his encouragement and careful guidance, and to Chenyang Ma for many useful discussions. We also thank the referee for helpful comments.

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