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arXiv · 1212.4070

On the definition of the Galois group of linear differential equations

Katsunori Saito
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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.

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Katsunori Saito. 2012-12-17. On the definition of the Galois group of linear differential equations. https://arxiv.org/abs/1212.4070

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