Galois algebras and their homomorphisms.
Galois cohomology of biquadratic extensions.
Galois cohomology of special orthogonal groups.
Galois cohomology of the classical gorups over fields of cohomological dimension ... 2.
Galois Coverings of the Non-Archimedean Projective Line.
Galois Covers and the Hilbert-Grunwald Property
Our main result combines three topics: it contains a Grunwald-Wang type conclusion, a version of Hilbert’s irreducibility theorem and a -adic form à la Harbater, but with good reduction, of the Regular Inverse Galois Problem. As a consequence we obtain a statement that questions the RIGP over . The general strategy is to study and exploit the good reduction of certain twisted models of the covers and of the associated moduli spaces.
Galois covers of over with prescribed local or global behavior by specialization
This paper considers some refined versions of the Inverse Galois Problem. We study the local or global behavior of rational specializations of some finite Galois covers of .
Galois covers with prescribed fibers : the Beckmann-Black problem
Galois Extensions with Bounded Ramifaction in Characteristic p. On a question of S. Abhyankar.
Galois groups and connection matrices for -difference equations.
Galois groups and elementary solutions of some linear differential equations.
Galois groups of trinomials
Galois module structure of Milnor -theory mod in characteristic .
Galois modules and embedding problems.
Galois properties of linear differential equations
Galois realizability of groups of order 64
This article examines the realizability of groups of order 64 as Galois groups over arbitrary fields. Specifically, we provide necessary and sufficient conditions for the realizability of 134 of the 200 noncyclic groups of order 64 that are not direct products of smaller groups.
Galois realizability of groups of orders p 5 and p 6
Let p be an odd prime and k an arbitrary field of characteristic not p. We determine the obstructions for the realizability as Galois groups over k of all groups of orders p 5 and p 6 that have an abelian quotient obtained by factoring out central subgroups of order p or p 2. These obstructions are decomposed as products of p-cyclic algebras, provided that k contains certain roots of unity.
Galois realization of central extensions of the symmetric group with kernel a cyclic 2-group
Galois representations, embedding problems and modular forms.
To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations...
Galois representations on profinite braid groups on curves.