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
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