Abstract
A class of linear systems which after ordinary linear systems are in a certain sense the simplest ones, is associated with every algebraic function field. From the standpoint developed in this paper ordinary linear systems are associated with the rational function field.
Similar content being viewed by others
References
M.F. Atiyah and I.G. McDonald, Introduction to commutative algebra.Addison-Wesley, Reading, MA, 1969.
N. Bourbaki, Algebre commutative. Éléments de Mathématique, Chap. 1–7.Hermann, Paris, 1961–1965.
C. Chevalley, Introduction to the theory of algebraic functions of one variable.American Mathematical Society, New York, 1951.
H. Grauert and R. Remmert, Theorie der Steinschen Räume.Springer-Verlag, New York, 1977.
A. Grothendieck, Local cohomology. Lecture Notes in Mathematics, v.41.Springer-Verlag, Berlin, 1967.
R. Hartshorne, Algebraic geometry. Graduate Texts in Mathematics, v.52.Springer-Verlag, New York, 1977.
R. Hermann, Topics in the geometric theory of linear systems. Interdisciplinary Mathematics, v.22.Math. Sci. Press, Brookline, MA, 1985.
S. Lang, Algebra.Addison-Wesley, Reading, MA, 1965.
V.G. Lomadze, Finite-dimensional time invariant linear dynamical systems: Algebraic theory.Acta Applicandae Mathematicae 19 (1990), 149–201.
V.G. Lomadze, Linear systems and coherent sheaves. (Russian)Bull. Acad. Sci. Georgian SSR,126(1987), No. 1, 37–40.
J.P. Serre, Groupes algebriques et corps de classes.Hermann, Paris, 1969.
A. Weil, Basic number theory. Grundlehren der Mathematischen Wissenschaften, Bd. 144.Springer-Verlag, New York, 1967.