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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Frobenius-Perron theory for projective schemes
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by J. M. Chen, Z. B. Gao, E. Wicks, J. J. Zhang, X. H. Zhang and H. Zhu HTML | PDF
Trans. Amer. Math. Soc. 376 (2023), 2293-2324 Request permission

Abstract:

The Frobenius-Perron theory of an endofunctor of a $\Bbbk$-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.
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Additional Information
  • J. M. Chen
  • Affiliation: School of Mathematical Sciences, Xiamen University, Xiamen 361005, Fujian, People’s Republic of China
  • ORCID: 0000-0002-2131-7782
  • Email: chenjianmin@xmu.edu.cn
  • Z. B. Gao
  • Affiliation: Department of Communication Engineering, Xiamen University, Xiamen 361005, Fujian, People’s Republic of China
  • ORCID: 0000-0003-1878-9065
  • Email: gaozhibin@xmu.edu.cn
  • E. Wicks
  • Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195
  • MR Author ID: 1310352
  • Email: elizabethlwicks@gmail.com
  • J. J. Zhang
  • Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195
  • MR Author ID: 314509
  • Email: zhang@math.washington.edu
  • X. H. Zhang
  • Affiliation: College of Sciences, Ningbo University of Technology, Ningb 315211, Zhejiang, People’s Republic of China
  • Email: zhang-xiaohong@t.shu.edu.cn
  • H. Zhu
  • Affiliation: Department of Information Sciences, the School of Mathematics and Physics, Changzhou University, Changzhou 213164, Jiangsu, People’s Republic of China
  • Email: zhuhongazhu@aliyun.com
  • Received by editor(s): April 29, 2020
  • Received by editor(s) in revised form: December 10, 2021
  • Published electronically: January 18, 2023
  • Additional Notes: The first author was partially supported by the National Natural Science Foundation of China (Grant Nos. 11971398 and 12131018) and the Fundamental Research Funds for Central Universities of China (Grant No. 20720180002). The second author was partially supported by the National Natural Science Foundation of China (Grant No. 61971365). The third and fourth authors were partially supported by the US National Science Foundation (Grant Nos. DMS-1402863, DMS-1700825 and DMS-2001015). The fifth author was partially supported by the National Natural Science Foundation of China (Grant No. 11401328). The sixth author was partially supported by a grant from Jiangsu overseas Research and Training Program for university prominent young and middle-aged Teachers and Presidents, China
  • © Copyright 2023 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 376 (2023), 2293-2324
  • MSC (2020): Primary 16E35, 16E65, 16E10; Secondary 16B50
  • DOI: https://doi.org/10.1090/tran/8624
  • MathSciNet review: 4557866