5 papers
Conjecture I for unirational algebraic groups over imperfect fields
Alexandre Lourdeaux, Anis Zidani
Serre's Conjecture I states that the first Galois cohomology set of any smooth connected linear algebraic group is trivial over a perfect field of cohomological dimension at most 1…
Cohomological invariants of hermitian forms that detect hyperbolicity
Yong Hu, Alexandre Lourdeaux
By using unramified cohomology groups, we construct a full sequence of cohomological invariants for hermitian forms of any (orthogonal, symplectic or unitary) type that can be used…
A characterization of groups of type arising from the first Tits construction
Vladimir Chernousov, Alexandre Lourdeaux, Arturo Pianzola
We show that algebraic groups of type (or equivalently Albert algebras) arising from the first Tits construction are determined uniquely by their invariant.
Degree 2 cohomological invariants of linear algebraic groups
Alexandre Lourdeaux
The paper deals with the cohomological invariants of smooth and connected linear algebraic groups over an arbitrary field. More precisely, we study degree invariants with coeff…
On geometry of some pseudo-reductive groups
Alexandre Lourdeaux
Based on the work of Conrad-Gabber-Prasad, the paper deals with the geometry of particular pseudo-semisimple groups, namely those which can be written as quotient of Weil restricti…