  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.
