Philippe Gille

collaborators

2 papers

math.NT2025

The power operation in the Galois cohomology of a reductive group over a number field

Mikhail Borovoi, Zinovy Reichstein, Philippe Gille

For a connected reductive group $G$ over a local or global field $K$ , we define a *diamond* (or *power*) operation $$(Î¾,n)\mapsto Î¾^{\Diamond n}\,\colon\, H^1(K,G)\times {\mathbb…

math.RA2025

Central simple algebras, Milnor $K$ -theory and homogeneous spaces over complete discretely valued fields of dimension 2

Philippe Gille, Diego Izquierdo, Giancarlo Lucchini Arteche

Let $K$ be a complete discretely valued field with residue field $K ˉ$ of dimension $1$ (not necessarily perfect). This occurs if and only if $K$ has dimension $2$ . We prove the…

The power operation in the Galois cohomology of a reductive group over a number field

Central simple algebras, Milnor K-theory and homogeneous spaces over complete discretely valued fields of dimension 2

Central simple algebras, Milnor $K$ -theory and homogeneous spaces over complete discretely valued fields of dimension 2