Journal of the
Korean Mathematical Society JKMS

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)