English

Frobenius-Perron theory for projective schemes

Rings and Algebras 2021-12-17 v3

Abstract

The Frobenius-Perron theory of an endofunctor of a k\Bbbk-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.

Keywords

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}
}

Comments

31 pages

R2 v1 2026-06-23T10:11:55.603Z