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Comptes Rendus Mathématique
Volume 353, n° 1
pages 57-61 (janvier 2015)
Doi : 10.1016/j.crma.2014.10.007
Received : 21 July 2014 ;  accepted : 13 October 2014
Functional calculus on Nœtherian schemes
Calcul fonctionnel sur les schémas nœthériens
 

Anar Dosi
 Middle East Technical University Northern Cyprus Campus, Guzelyurt, KKTC, Mersin 10, Turkey 

Abstract

The present note is devoted to the functional calculus problem for sections of a quasi-coherent sheaf on a Nœtherian scheme. We prove scheme-theoretic analogs of the known results on the multivariable holomorphic functional calculus over Fréchet modules which are mainly due to of J. Taylor and M. Putinar. The generalization of the Taylor joint spectrum considered in the paper leads to subvarieties of an algebraic variety over an algebraically closed field. In particular, every algebraic variety is represented as the joint spectrum of related coordinate multiplication operators.

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Résumé

La présente Note est consacrée à un problème de calcul fonctionnel sur les sections d'un faisceau quasi cohérent d'un schéma nœthérien. Nous démontrons des analogues des résultats connus du calcul fonctionnel holomorphe en plusieurs variables sur les modules de Fréchet, essentiellement dus à J. Taylor et M. Putinar. Nous considérons un analogue du spectre joint de Taylor dans un cadre très général, conduisant à des sous-variétés d'une variété algébrique sur un corps algébriquement clos. En particulier, toute variété algébrique est réalisée comme le spectre joint des opérateurs de multiplication par les coordonnées correspondantes.

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