Weighted projective lines with weight permutation
J. Korean Math. Soc. 2021 Vol. 58, No. 1, 219-236
Published online November 19, 2020
Printed January 1, 2021
Lina Han, Xintian Wang
Tsinghua University; China University of Mining and Technology (Beijing)
Abstract : Let $\mathbb X$ be a weighted projective line defined over the algebraic closure $k=\overline{\mathbb F}_q$ of the finite field $\bbf_q$ and $\sigma$ be a weight permutation of $\mathbb X$. By folding the category coh-$\mathbb{X}$ of coherent sheaves on $\mathbb X$ in terms of the Frobenius twist functor induced by $\sigma$, we obtain an $\bbf_q$-category, denoted by coh-$(\mathbb{X},\sigma;q)$. We then prove that $\coh(\mathbb{X},\sigma;q)$ is derived equivalent to the valued canonical algebra associated with $(\bbX,\sigma)$.
Keywords : Weighted projective line, weight permutation, Frobenius twist functor
MSC numbers : 18E30, 16G20
Supported by : This work was financially supported by the Natural Science Foundation of China (Grant Nos. 11971255, 11901567) and the Fundamental Research Funds for the Central Universities, China (No. 2019QS01)
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