Solvable-by-finite groups as differential Galois groups
Stokes phenomenon, multisummability and differential Galois groups
We precise the cohomological analysis of the Stokes phenomenon for linear differential systems due to Malgrange and Sibuya by making a rigid natural choice of a unique cocycle (called a Stokes cocyle) in every cohomological class. And we detail an algebraic algorithm to reduce any cocycle to its cohomologous Stokes form. This gives rise to an almost algebraic definition of sums for formal solutions of systems which we compare to the most usual ones. We also use this construction to the Stokes cocycle...
Strong normality and normality for difference fields.
Suite spectrale d'une fibration
Sur certaines algèbres de Lie de dérivations
Il est démontré que toute a.d.g.c. ayant un modèle minimal de Sullivan de type fini peut être représentée par une certaine algèbre de Lie différentielle graduée de dérivations. En particulier on peut ainsi représenter le type d’homotopie rationnelle d’un espace topologique.
Sur la cohomologie de l'algèbre de Lie des champs de vecteurs
Sur les formes différentielles associées
The constants of the Volterra derivation
The ring of constants of the Volterra derivation is found. Confirming a conjecture of Zielinski, it is always a polynomial ring.
The differential spectrum of a ring
The five-variable Volterra system
We give a description of all polynomial constants of the five-variable Volterra derivation, hence of all polynomial first integrals of its corresponding Volterra system of differential equations. The Volterra system plays a significant role in plasma physics and population biology.
The fourteenth problem of Hilbert for polynomial derivations
We present some facts, observations and remarks concerning the problem of finiteness of the rings of constants for derivations of polynomial rings over a commutative ring k containing the field ℚ of rational numbers.
The Global Homological Dimension of Some Algebras of Differential Operators.
The Lamé family of connections on the projective line
This paper deals with rank two connections on the projective line having four simple poles with prescribed local exponents 1/4 and . This Lamé family of connections has been extensively studied in the literature. The differential Galois group of a Lamé connection is never maximal : it is either dihedral (finite or infinite) or reducible. We provide an explicit moduli space of those connections having a free underlying vector bundle and compute the algebraic locus of those reducible connections....
The Picard-Vessiot closure in differential Galois theory
The Set of Derivatives in a Non-Archimedean Field.
The structure of strongly normal difference extensions.
Théories cohomologiques.
Théories de Galois différentielles et transcendance
On décrit des preuves galoisiennes des versions logarithmique et exponentielle de la conjecture de Schanuel, pour les variétés abéliennes sur un corps de fonctions.
Travaux récents de Ju. V. Nesterenko
Two remarks about Picard-Vessiot extensions and elementary functions
We present a simple proof of the theorem which says that for a series of extensions of differential fields K ⊂ L ⊂ M, where K ⊂ M is Picard-Vessiot, the extension K ⊂ L is Picard-Vessiot iff the differential Galois group is a normal subgroup of . We also present a proof that the probability function Erf(x) is not an elementary function.