The inverse problem of differential Galois theory over the field R(z)
| dc.creator | Dyckerhoff, Tobias | |
| dc.date | 2008-02-20 | |
| dc.date.accessioned | 2026-07-07T09:22:06Z | |
| dc.date.available | 2026-07-07T09:22:06Z | |
| dc.description | 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 $\mathbb{C}(z)$. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/0802.2897 | |
| dc.identifier | http://arxiv.org/abs/0802.2897 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155257 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Algebraic Geometry | |
| dc.title | The inverse problem of differential Galois theory over the field R(z) | |
| dc.type | text |