Displaying similar documents to “On a general difference Galois theory II”

Morales-Ramis Theorems Malgrange pseudogroup

Guy Casale (2009)

Annales de l’institut Fourier

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In this article we give an obstruction to integrability by quadratures of an ordinary differential equation on the differential Galois group of variational equations of any order along a particular solution. In Hamiltonian situation the condition on the Galois group gives Morales-Ramis-Simó theorem. The main tools used are Malgrange pseudogroup of a vector field and Artin approximation theorem.

On a general difference Galois theory I

Shuji Morikawa (2009)

Annales de l’institut Fourier

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We know well difference Picard-Vessiot theory, Galois theory of linear difference equations. We propose a general Galois theory of difference equations that generalizes Picard-Vessiot theory. For every difference field extension of characteristic 0 , we attach its Galois group, which is a group of coordinate transformation.

A Galois D -groupoid for q -difference equations

Anne Granier (2011)

Annales de l’institut Fourier

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We first recall Malgrange’s definition of D -groupoid and we define a Galois D -groupoid for q -difference equations. Then, we compute explicitly the Galois D -groupoid of a constant linear q -difference system, and show that it corresponds to the q -difference Galois group. Finally, we establish a conjugation between the Galois D -groupoids of two equivalent constant linear q -difference systems, and define a local Galois D -groupoid for Fuchsian linear q -difference systems by giving its realizations. ...

Dynamics on Character Varieties and Malgrange irreducibility of Painlevé VI equation

Serge Cantat, Frank Loray (2009)

Annales de l’institut Fourier

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We consider representations of the fundamental group of the four punctured sphere into SL ( 2 , ℂ ) . The moduli space of representations modulo conjugacy is the character variety. The Mapping Class Group of the punctured sphere acts on this space by symplectic polynomial automorphisms. This dynamical system can be interpreted as the monodromy of the Painlevé VI equation. Infinite bounded orbits are characterized: they come from SU ( 2 ) -representations. We prove the absence of invariant affine structure...

Which weakly ramified group actions admit a universal formal deformation?

Jakub Byszewski, Gunther Cornelissen (2009)

Annales de l’institut Fourier

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Consider a representation of a finite group G as automorphisms of a power series ring k [ [ t ] ] over a perfect field k of positive characteristic. Let D be the associated formal mixed-characteristic deformation functor. Assume that the action of G is weakly ramified, i.e., the second ramification group is trivial. Example: for a group action on an ordinary curve, the action of a ramification group on the completed local ring of any point is weakly ramified. ...