Frobenius-Perron theory for projective schemes

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

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Frobenius-Perron theory for projective schemes

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arxiv 1907.02221 v3 pith:4RAR3KLV submitted 2019-07-04 math.RA

J.M. Chen , Z.B. Gao , E. Wicks , J. J. Zhang , X-.H. Zhang , H. Zhu This is my paper

classification math.RA

keywords frobenius-perroncategoriesprojectivetheoryderivedinvariantsschemesabelian

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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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