Operator index of a nonsingular algebraic curve

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DOSİ A.

Turkish Journal of Mathematics, vol.47, no.7, pp.1991-2005, 2023 (SCI-Expanded, Scopus, TRDizin) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 7
  • Publication Date: 2023
  • Doi Number: 10.55730/1300-0098.3477
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1991-2005
  • Keywords: Algebraic variety, Dedekind extension, index of an operator tuple, integral extension, Koszul homology groups of a variety, Taylor spectrum
  • Open Archive Collection: AVESIS Open Access Collection
  • Middle East Technical University Affiliated: Yes

Abstract

The present paper is devoted to a scheme-theoretic analog of the Fredholm theory. The continuity of the index function over the coordinate ring of an algebraic variety is investigated. It turns out that the index is closely related to the filtered topology given by finite products of maximal ideals. We prove that a variety over a field possesses the index function on nonzero elements of its coordinate ring iff it is an algebraic curve. In this case, the index is obtained by means of the multiplicity function from its normalization if the ground field is algebraically closed.