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Frobenius-Perron theory for projective schemes

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 نشر من قبل Jianmin Chen
 تاريخ النشر 2019
  مجال البحث
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The Frobenius-Perron theory of an endofunctor of a $Bbbk$-linear category (recently introduced in cite{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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