On the definition of the Galois group of linear differential equations [article]

Katsunori Saito
2012 arXiv   pre-print
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.
arXiv:1212.4070v1 fatcat:m6up2srowzhhbkqtrkajsuvkny