Frobenius-Perron theory for projective schemes
Rings and Algebras
2021-12-17 v3
Abstract
The Frobenius-Perron theory of an endofunctor of a -linear category (recently introduced in [CG]) 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.
Cite
@article{arxiv.1907.02221,
title = {Frobenius-Perron theory for projective schemes},
author = {J. M. Chen and Z. B. Gao and E. Wicks and J. J. Zhang and X-. H. Zhang and H. Zhu},
journal= {arXiv preprint arXiv:1907.02221},
year = {2021}
}
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31 pages