Weighted projective lines with weight permutation
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초록
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 $(\bbX,\sigma)$.
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 $(\bbX,\sigma)$.
참고문헌 (15)
- Xiao-Wu Chen, "Derived equivalences via HRS-tilting", Advances in Mathematics, 354, pp.106749~ (2019), Elsevier BV[DOI]
- X.-W. Chen, "Introduction to coherent sheaves over weighted projective lines", arXiv: 0911.4473., ~
- Zhengxin Chen, "A realization of elliptic Lie algebras of type F (2,2)4by the RingelHall approach", Journal of Algebra, 350(1), pp.108~131 (2012), Elsevier BV[DOI]
- X.-W. Chen, "Hereditary triangulated categories", J. Noncommut. Geom, 12(4), pp.1425~1444 (2018)[DOI]
- Bangming Deng, "Frobenius morphisms and representations of algebras", Transactions of the American Mathematical Society, 358(8), pp.3591~3622 (2006), American Mathematical Society (AMS)[DOI]
- Bangming Deng, "Folding derived categories with Frobenius functors", Journal of Pure and Applied Algebra, 208(3), pp.1023~1050 (2007), Elsevier BV[DOI]
- B. Deng, "Finite dimensional algebras and quantum groups" (2008), American Mathematical Society
- A. D. Elagin, "On equivariant triangulated categories", arXiv:1403.7027v2, ~ (2015)
- W. Geigle, "Singularities, representation of algebras, and vector bundles" (2006), Springer
- D. Happel, "Tilting in abelian categories and quasitilted algebras", Mem. Amer. Math. Soc, 120(57), pp.viii~88 (1996)[DOI]
- Dieter Happel, "Tilted Algebras", Transactions of the American Mathematical Society, 274(2), pp.399~ (1982), JSTOR[DOI]
- B. Keller, "Sous les cat´egories d´eriv´ees", C. R. Acad. Sci. Paris S´er. I Math, 305(6), pp.225~228 (1987)
- I. Reiten, "Noetherian hereditary abelian categories satisfying Serre duality", Journal of the American Mathematical Society, 15(2), pp.295~366 (2002), American Mathematical Society (AMS)[DOI]
- C. M. Ringel, "Topics in algebra, Part 1", pp.407~432 (1988), Banach Center Publ
- Jean-Pierre Serre, "Faisceaux Algebriques Coherents", The Annals of Mathematics, 61(2), pp.197~ (1955), JSTOR[DOI]