The spectrum of a module along scheme morphism and multi-operator functional calculus

The present paper is devoted to a scheme-theoretic version of holomorphic multi-operator functional calculus. We construct a functional calculus with sections of a quasi-coherent sheaf on a noetherian scheme, and prove analogs of the known results from multivariable holomorphic functional calculus over Fréchet modules. A spectrum of an algebraic variety over an algebraically closed field is considered. This concept reflects Taylor joint spectrum from operator theory. Every algebraic variety turns out to be a joint spectrum of the coordinate multiplication operators over its coordinate ring.