Moscow Mathematical Journal

Volume 21, Issue 2, April–June 2021 pp. 287–323.

The Spectrum of a Module along Scheme Morphism and Multi-Operator Functional Calculus

Authors: Anar Dosi (1)
Author institution:(1) Middle East Technical University Northern Cyprus Campus, Guzelyurt, KKTC, Mersin 10, Turkey

Summary:

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.

2020 Math. Subj. Class. Primary: 14A15, 14F06; Secondary: 13D02, 46H30, 13D05.

Keywords: Noetherian schemes, quasi-coherent sheaf, spectrum of a module, sheaf cohomology.

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