Base change for Picard–Vessiot closures
Volume 94 / 2011
Banach Center Publications 94 (2011), 233-238
MSC: 12H05.
DOI: 10.4064/bc94-0-16
Abstract
The differential automorphism group, over $F$, $\Pi_1(F_1)$ of the Picard–Vessiot closure $F_1$ of a differential field $F$ is a proalgebraic group over the field $C_F$ of constants of $F$, which is assumed to be algebraically closed of characteristic zero, and its category of $C_F$ modules is equivalent to the category of differential modules over $F$. We show how this group and the category equivalence behave under a differential extension $E \supset F$, where $C_E$ is also algebraically closed.
