## 53 Citations

The behaviour of the differential Galois group on the generic and special fibres: A Tannakian approach

- Mathematics
- 2009

Let o be a complete DVR of fraction field K and algebraically closed residue field k. Let A be an o-adic domain which is smooth and topologically of finite type. Let D be the ring of o-linear…

A general theory of André’s solution algebras

- Mathematics
- 2020

We extend Yves Andre's theory of solution algebras in differential Galois theory to a general Tannakian context. As applications, we establish analogues of his correspondence between solution fields…

The behaviour of the differential Galois group on the generic and special fibres: A Tannakian approach

- Mathematics
- 2009

Let o be a complete DVR of fraction field K and algebraically closed residue field k. Let A be an o-adic domain which is smooth and topologically of finite type. Let D be the ring of o-linear…

Hyperdifferential Properties of Drinfeld Quasi-Modular Forms

- Mathematics
- 2007

This article is divided in two parts. In the first part we endow a certain ring of ``Drinfeld quasi-modular forms'' for $\GL_2(\FF_q[T])$ (where $q$ is a power of a prime) with a system of ``divided…

Lifting $D$-modules from positive to zero characteristic

- Mathematics
- 2011

Nous etudions des relevements des D-modules (D est l'anneau des operateurs differentiels de EGA IV) de la caracteristique positive en caracteristique nulle en utilisant des idees de Matzat et la…

On the finite inverse problem in iterative differential Galois theory

- Mathematics
- 2010

In positive characteristic, nearly all Picard-Vessiot extensions are inseparable over some intermediate iterative differential extensions. In the Galois correspondence, these intermediate fields…

Local solutions to positive characteristic non-Archimedean differential equations

- MathematicsCompositio Mathematica
- 2007

Abstract In the complex domain, one can integrate (solve) holomorphic ordinary differential equations (ODEs) near a non-singular point. We study the existence of solutions in the case of a positive…

Stratified Bundles on Curves and Differential Galois Groups in Positive Characteristic

- MathematicsSymmetry, Integrability and Geometry: Methods and Applications
- 2019

A variety $X$ over a field of characteristic $p>0$ has a stratified (regular singular) fundamental group which plays a role similar to the topological fundamental group in the complex…

Integral p-adic Differential Modules

- Mathematics
- 2007

— An integral (or bounded) local D-module is a differential module over a local D-ring R having congruence solution bases over R. In case R is equipped with an iterative derivation, such a D-module…

Differential modules and dormant opers of higher level

- Mathematics
- 2022

In the first half of the present paper, we study higher-level generalizations of differential modules in positive characteristic. These objects may be regarded as ring-theoretic counterparts of…

## References

SHOWING 1-10 OF 12 REFERENCES

Galois Theory of Differential Equations, Algebraic Groups and Lie Algebras

- MathematicsJ. Symb. Comput.
- 1999

The Galois theory of linear differential equations is presented, including full proofs. The connection with algebraic groups and their Lie algebras is given. As an application the inverse problem of…

Fundamental Groups of Curves in Characteristic p

- Mathematics
- 1995

Consider the following general problem: Given a smooth affine curve U over an algebraically closed field k, find the fundamental group πA(U). When k = C, U is a Riemann surface, and π1 can be…

Nice equations for nice groups

- Mathematics
- 1994

Nice trinomial equations are given for unramified coverings of the affine line in nonzero characteristicp with PSL(m,q) and SL(m,q) as Galois groups. Likewise, nice trinomial equations are given for…

On the deformation of Artin-Schreier to Kummer

- Mathematics
- 1989

© Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1989, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www.…

Representations of algebraic groups

- Mathematics
- 1987

Part I. General theory: Schemes Group schemes and representations Induction and injective modules Cohomology Quotients and associated sheaves Factor groups Algebras of distributions Representations…

Linear Algebraic Groups

- Mathematics
- 1981

A linear algebraic group over an algebraically closed field k is a subgroup of a group GL n (k) of invertible n × n-matrices with entries in k, whose elements are precisely the solutions of a set of…