Real and p-adic Picard-Vessiot fields

Abstract

We consider differential modules over real and p-adic differential fields such that their field of constants is real closed (respectively p-adically closed). Using Deligne's work on Tannakian categories and a result of Serre on Galois cohomology, a purely algebraic proof of the existence and unicity of real (respectively p-adic) Picard-Vessiot fields is obtained.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1302.1012