Forms of Hopf algebras and Galois theory
Fractions rationnelles invariantes
Frattini Covers and Projective Groups Without the Extension Property.
Frattini-Einbettungsprobleme über Hilbertkörpern.
Freeness, linear disjointness, and implicitization -- a classical approach.
Frobenius modules and Galois representations
Frobenius modules are difference modules with respect to a Frobenius operator. Here we show that over non-archimedean complete differential fields Frobenius modules define differential modules with the same Picard-Vessiot ring and the same Galois group schemes up to extension by constants. Moreover, these Frobenius modules are classified by unramified Galois representations over the base field. This leads among others to the solution of the inverse differential Galois problem for -adic differential...
From p-rigid elements to valuations (with a Galois-characterization of p-adic fields).
Function Fileds of Pfister Forms.
Functoriality and the Inverse Galois problem II: groups of type and
This paper contains an application of Langlands’ functoriality principle to the following classical problem: which finite groups, in particular which simple groups appear as Galois groups over ? Let be a prime and a positive integer. We show that that the finite simple groups of Lie type if and appear as Galois groups over , for some divisible by . In particular, for each of the two Lie types and fixed we construct infinitely many Galois groups but we do not have a precise control...
Funktionenkörper mit isomorphen absoluten Galoisgruppen.
Fuzzy subfields.
Galois algebras and their homomorphisms.
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 module structure of Milnor -theory mod in characteristic .
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