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


Dosi A.

Moscow Mathematical Journal, vol.21, no.2, pp.287-323, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.17323/1609-4514-2021-21-2-287-323
  • Title of Journal : Moscow Mathematical Journal
  • Page Numbers: pp.287-323
  • Keywords: Noetherian schemes, quasi-coherent sheaf, spectrum of a module, sheaf cohomology, PROJECTIVE SPECTRUM, LIE-ALGEBRA, ELEMENTS

Abstract

© 2021 Independent University of Moscow.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 noe-therian scheme, and prove analogs of the known results from multivari-able 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. Ev-ery algebraic variety turns out to be a joint spectrum of the coordinate multiplication operators over its coordinate ring.