Affine C-ferential group schemes and parameterized Galois theory
- Affine C-ferential Gruppenschemata und parametrisierte Galois-Theorie
Ernst, Stefan; Hartmann, Julia (Thesis advisor)
Aachen : Publikationsserver der RWTH Aachen University (2014)
Dissertation / PhD Thesis
Aachen, Techn. Hochsch., Diss., 2014
In this thesis we develop a theory of differential algebraic groups without any assumptions on the base field and its characteristic. Further we develop a parameterized Picard-Vessiot theory (also without any assumptions on the base field and its characteristic) by using a Hopf algebraic approach. In particular, we obtain a Galois correspondence and the arising Galois groups are this differential algebraic groups. Also we give some first examples to the inverse problem and explain the connection between parameterized differential equations and this parameterized Picard-Vessiot theory.