The inverse problem of differential Galois theory over the field R(z)

Autor:	Dyckerhoff, Tobias
Rok vydání:	2008
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Algebraic Geometry
Druh dokumentu:	Working Paper
Popis:	We describe a Picard-Vessiot theory for differential fields with non algebraically closed fields of constants. As a technique for constructing and classifying Picard-Vessiot extensions, we develop a Galois descent theory. We utilize this theory to prove that every linear algebraic group $G$ over $\mathbb{R}$ occurs as a differential Galois group over $\mathbb{R}(z)$. The main ingredient of the proof is the Riemann-Hilbert correspondence for regular singular differential equations over $\mathbb{C}(z)$. Comment: 23 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0802.2897 Zobrazit plný text záznamu View this record from Arxiv