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- Title
Operator index of a nonsingular algebraic curve.
- Authors
DOSI, Anar
- 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.
- Subjects
ALGEBRAIC curves; RING theory
- Publication
Turkish Journal of Mathematics, 2023, Vol 47, Issue 7, p1991
- ISSN
1300-0098
- Publication type
Article
- DOI
10.55730/1300-0098.3477