Corpus ID: 17140742

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

@article{Dyckerhoff2008TheIP,
  title={The inverse problem of differential Galois theory over the field R(z)},
  author={Tobias Dyckerhoff},
  journal={arXiv: Classical Analysis and ODEs},
  year={2008}
}

Tobias Dyckerhoff

Published 2008

Mathematics

arXiv: Classical Analysis and ODEs

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… CONTINUE READING

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