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

Abstract:
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 $\mathbb{C}(z)$.

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publication date:
2008-02-20
Source identifiers:
398221
Keywords:
Pubs id:
pubs:398221
UUID:
uuid:0302e011-7c1f-45cc-bb3b-4eedea81b0d5
Local pid:
pubs:398221
Deposit date:
2013-11-16

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