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arXiv · 1907.02221

Frobenius-Perron theory for projective schemes

J. M. Chen·Z. B. Gao·E. Wicks·J. J. Zhang·X-. H. Zhang·H. Zhu
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Abstract

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

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BibTeXRIS

J. M. Chen, Z. B. Gao, E. Wicks, J. J. Zhang, X-. H. Zhang, H. Zhu. 2019-07-04. Frobenius-Perron theory for projective schemes. https://arxiv.org/abs/1907.02221

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