Cohomologie galoisienne : progrès et problèmes
Differential equations and algebraic transcendents: french efforts at the creation of a Galois theory of differential equations 1880–1910
A “Galois theory” of differential equations was first proposed by Émile Picard in 1883. Picard, then a young mathematician in the course of making his name, sought an analogue to Galois’s theory of polynomial equations for linear differential equations with rational coefficients. His main results were limited by unnecessary hypotheses, as was shown in 1892 by his student Ernest Vessiot, who both improved Picard’s results and altered his approach, leading Picard to assert that his lay closest to...
Fields: Algebraically closed and others.
Groupes de Galois sur
O devátém Hilbertově problému
On realizability of p-groups as Galois groups
2000 Mathematics Subject Classification: 12F12, 15A66.In this article we survey and examine the realizability of p-groups as Galois groups over arbitrary fields. In particular we consider various cohomological criteria that lead to necessary and sufficient conditions for the realizability of such a group as a Galois group, the embedding problem (i.e., realizability over a given subextension), descriptions of such extensions, automatic realizations among p-groups, and related topics.
On the inverse problem of Galois theory.
The problem of the construction of number fields with Galois group over Q a given finite groups has made considerable progress in the recent years. The aim of this paper is to survey the current state of this problem, giving the most significant methods developed in connection with it.
Problèmes de nombres de classes de corps quadratiques imaginaires
Recent work on differential Galois theory
Solved and unsolved problems οn polynomials
Some Recent Developments in three Classical Problems of Number Theory.
Théorie algébrique de la croissance
Über die absolute Galoisgruppe algebraischer Zahlkörper.