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 Weighted projective lines with weight permutation J. Korean Math. Soc.Published online November 19, 2020 Lina Han and 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 Full-Text :

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