Differential equations, difference equations and algebraic relations: An extension to a theorem of Compoint
Commutative Algebra
2010-09-15 v1
Abstract
Let C be an algebraically closed field and X a projective curve over C. Consider an ordinary linear differential equation, or a linear differ- ence equation, with coefficients in the field of rational functions of X, and assume that its Galois Group G has finite determinant group and is reductive. In this context, the ideal of algebraic relations satisfied by a full system of solutions is generated by the G-invariants it contains. This result extends a theorem of E. Compoint.
Keywords
Cite
@article{arxiv.1009.2538,
title = {Differential equations, difference equations and algebraic relations: An extension to a theorem of Compoint},
author = {Camilo Sanabria},
journal= {arXiv preprint arXiv:1009.2538},
year = {2010}
}