On the definition of the Galois group of linear differential equations

Published 17 Dec 2012 in math.AG and math.AC | (1212.4070v1)

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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Authors (1)

Katsunori Saito

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