Arne Ledet

Brauer Type Embedding Problems

Galois theory Inverse Galois theory and embedding problems Brauer groups Group cohomology Quadratic forms Decomposing the obstruction Quadratic forms and embedding problems Reducing the embedding problem Pro-finite Galois theory Bibliography Index.

Generic Extensions and Generic Polynomials

We prove that the existence of generic polynomials and generic extensions are equivalent over an infinite field.

On the Essential Dimension of Some Semi-Direct Products

We give an upper bound on the essential dimension of the group Z=qo (Z=q) over the rational numbers, when q is a prime power.

Embedding problems with cyclic kernel of order 4

We consider Galois theoretical embedding problems with kernelC4, and prove that such an embedding problem can be ‘constructively’ reduced to two embedding problems, where the kernels are groups of roots of unity.

Generic polynomials for quasi-dihedral, dihedral and modular extensions of order 16

We describe Galois extensions where the Galois group is the quasidihedral, dihedral or modular group of order 16, and use this description to produce generic polynomials.

On the Essential Dimension of p -Groups

We improve the known bounds on the essential dimension of p-groups over (large) fields of characteristic p.

Generic and Explicit Realization of Smallp-groups

We prove the existence of a generic polynomial for the Heisenberg groupHp3 over a field of characteristic not p, where p is an odd prime.

On p-Groups in Characteristic p

We produce generic polynomials for p-groups over the prime field Fp with a small number of parameters.

Surjectivities, octonions and differential Galois theory

ABSTRACT We provide an explicit description of the torsors associated to the three groups related to the octonions—the exceptional Lie group G2 and the spin groups Spin7 and Spin8—and construct generic differential Galois extensions for those groups.

Generic Picard–Vessiot Extensions for Nonconnected Groups

Let K be a differential field with algebraically closed field of constants 𝒞 and G a linear algebraic group over 𝒞. We provide a characterization of the K-irreducible G-torsors for nonconnected groups G in terms of the first Galois cohomology H1(K, G) and use it to construct Picard–Vessiot extensions which correspond to nontrivial torsors for the infinite quaternion group, the infinite multiplicative and additive dihedral groups and the orthogonal groups. The extensions so constructed are generic for those groups.