Frobenius-Perron theory for projective schemes
Frobenius-Perron theory for projective schemes
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DOI：
10.1090/tran/8624
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发表时间：
2019-07
影响因子：
1.3
通讯作者：
J. Chen;Z. Gao;E. Wicks;J. J. Zhang-J.;X-.H. Zhang;H. Zhu
中科院分区：
文献类型：
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作者：
J. Chen;Z. Gao;E. Wicks;J. J. Zhang-J.;X-.H. Zhang;H. Zhu
k \Bbbk -线性范畴的内函子的Frobenius-Perron理论（最近在Chen et al. [Algebra Number Theory 13（2019），pp. 2005-2055]）为阿贝尔和三角范畴提供了新的不变量。在这里，我们研究Frobenius-Perron型不变量的衍生类别的交换和非交换投影计划。特别是，我们计算的Frobenius-Perron维数国内和管状加权投影线，定义Frobenius-Perron推广的Calabi-Yau和科代拉尺寸，并提供例子。我们将这一理论应用于与某些阿廷-舍尔特正则和有限维代数相关的派生范畴。
The Frobenius-Perron theory of an endofunctor of a k \Bbbk -linear category (recently introduced in Chen et al. [Algebra Number Theory 13 (2019), pp. 2005–2055]) provides new invariants for abelian and triangulated categories. Here we study Frobenius-Perron type invariants for derived categories of commutative and noncommutative projective schemes. In particular, we calculate the Frobenius-Perron dimension for domestic and tubular weighted projective lines, define Frobenius-Perron generalizations of Calabi-Yau and Kodaira dimensions, and provide examples. We apply this theory to the derived categories associated to certain Artin-Schelter regular and finite-dimensional algebras.