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Mathematische Zeitschrift

, Volume 288, Issue 1–2, pp 361–381 | Cite as

New classes of parameterized differential Galois groups

  • Annette Bachmayr
Article
  • 82 Downloads

Abstract

This paper is on the inverse parameterized differential Galois problem. We show that surprisingly many groups do not occur as parameterized differential Galois groups over K(x) even when K is algebraically closed. We then combine the method of patching over fields with a suitable version of Galois descent to prove that certain groups do occur as parameterized differential Galois groups over k((t))(x). This class includes linear differential algebraic groups that are generated by finitely many unipotent elements and also semisimple connected linear algebraic groups.

Keywords

Parameterized Picard–Vessiot theory Patching Linear differential algebraic groups Inverse differential Galois problem Galois descent 

Mathematics Subject Classification

12H05 20G15 14H25 34M50 34M03 34M15 

Notes

Acknowledgements

I wish to thank Michael F. Singer for helpful discussions concerning subgroups of \(\mathbb {G}_m\) that do not occur as parameterized Picard–Vessiot groups over K(x).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Mathematisches Institut der Universität BonnBonnGermany

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