6 papers
Enhanced Koszul properties in Galois cohomology
Jan Minac, Marina Palaisti, Federico W. Pasini +1
We prove that Galois cohomology satisfies several surprisingly strong versions of Koszul properties, under a well known conjecture, in the finitely generated case. In fact, these v…
Relations in the maximal pro- quotients of absolute Galois groups
Jan Minac, Michael Rogelstad, Nguyen Duy Tan
We observe that some basic but fundamental constructions in Galois theory can be used to obtain some interesting restrictions on the structure of Galois groups of maximal -exten…
Koszul algebras and quadratic duals in Galois cohomology
Jan Minac, Federico W. Pasini, Claudio Quadrelli +1
We investigate the Galois cohomology of finitely generated maximal pro- quotients of absolute Galois groups. Assuming the well-known conjectural description of these groups, we…
Special unipotent groups are split
Nguyen Duy Tan
We show that over any field , a smooth unipotent algebraic -group is special if and only if it is -split.
Embedding problems with local conditions and the admissibility of finite groups
Nguyen Duy Tan
Let be a field of characteristic , which has infinitely many discrete valuations. We show that every finite embedding problem for $\Gal(k)$ with finitely many prescribed l…
On the essential dimension of unipotent algebraic groups
Nguyen Duy Tan
We give an upper bound for the essential dimension of a smooth unipotent algebraic group over an arbitrary field. We also show that over a field which is finitely generated ove…