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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 $(\bbX,\sigma)$.
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참고문헌 (15)
참고문헌 신청
Xiao-Wu Chen / 2019 / Derived equivalences via HRS-tilting / Advances in Mathematics 354:106749
X.-W. Chen / Introduction to coherent sheaves over weighted projective lines / arXiv: 0911.4473.
Zhengxin Chen / 2012 / A realization of elliptic Lie algebras of type F (2,2)4by the RingelHall approach / Journal of Algebra 350(1):108~131
X.-W. Chen / 2018 / Hereditary triangulated categories / J. Noncommut. Geom 12(4):1425~1444
Bangming Deng / 2006 / Frobenius morphisms and representations of algebras / Transactions of the American Mathematical Society 358(8):3591~3622
X.-W. Chen / Introduction to coherent sheaves over weighted projective lines / arXiv: 0911.4473.
Zhengxin Chen / 2012 / A realization of elliptic Lie algebras of type F (2,2)4by the RingelHall approach / Journal of Algebra 350(1):108~131
X.-W. Chen / 2018 / Hereditary triangulated categories / J. Noncommut. Geom 12(4):1425~1444
Bangming Deng / 2006 / Frobenius morphisms and representations of algebras / Transactions of the American Mathematical Society 358(8):3591~3622
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