On the definition of the Galois group of linear differential equations

2012/12/17 by Saito, Katsunori
#13B05(Primary) 12H05 #16W25(Secondary) #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1212.4070

Abstract

Let us consider a linear differential equation over a differential field K. For a differential field extension L/K generated by a fundamental system of the equation, we show that Galois group according to the general Galois theory of Umemura coincides with the Picard-Vessiot Galois group. This conclusion generalized the comparision theorem of Umemura and Casale.

Related

• Real Picard-Vessiot theory
• Galois theory of differential schemes
• A Root Parametrized Differential Equation for the Special Linear Group
• On the Definitions of Difference Galois Groups
• Algebraic groups as difference Galois groups of linear differential equations