On Linear Dependence Over Complete Differential Algebraic Varieties. Issue 6 (2nd June 2016)

• Record Type: Journal Article
• Authors: Freitag, James; Sánchez, Omar León; Simmons, William
• Is Part Of: Communications in algebra. Volume 44:Issue 6(2016)
• Page Start: 2645
• Page End: 2669
• Publication Date: 2016-06-02
• Subjects: Differential algebraic geometry -- Model theory; 12H05 -- 03C98; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2015.1057828
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract : We extend Kolchin's results from [12 ] on linear dependence over the constant points of projective algebraic varieties to linear dependence over arbitrary complete differential algebraic varieties. We show that in this more general setting, the notion of linear dependence still has necessary and sufficient conditions given by the vanishing of a certain system of differential-polynomials equations. We also discuss some conjectural questions around completeness and the catenary problem.