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
    23 Citations
    Large Fields in Differential Galois Theory.
    • 5
    • PDF
    A categorical approach to Picard-Vessiot theory
    • 4
    • PDF
    SOME DEFINABLE GALOIS THEORY AND EXAMPLES
    • 13
    • PDF
    Torsion group schemes as iterative differential Galois groups
    • PDF

    References

    SHOWING 1-10 OF 18 REFERENCES
    Representations of algebraic groups.
    • 736
    • PDF
    Algebraic function fields and codes
    • 1,734
    Introduction to Affine Group Schemes
    • 661
    Linear Algebraic Groups
    • 1,153
    • PDF
    Lectures on Riemann Surfaces
    • 591
    SpringerVerlag
    • Berlin-Heidelberg-New York,
    • 2003
    Connected groups as differential Galois groups
    • J. Algebra
    • 1996
    Catégories Tannakiennes, The Grothendieck Festschrift, Collect
    • Artic. in Honor of the 60th Birthday of A. Grothendieck. Vol. II, Birkhäuser,
    • 1990
    Differential Galois theory and tensor products
    • 18