Operator index of a nonsingular algebraic curve

Creative Commons License

DOSİ A.

Turkish Journal of Mathematics, cilt.47, sa.7, ss.1991-2005, 2023 (SCI-Expanded, Scopus, TRDizin) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47 Sayı: 7
  • Basım Tarihi: 2023
  • Doi Numarası: 10.55730/1300-0098.3477
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1991-2005
  • Anahtar Kelimeler: Algebraic variety, Dedekind extension, index of an operator tuple, integral extension, Koszul homology groups of a variety, Taylor spectrum
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.