Plongements d'espaces homogènes sphériques sur un corps quelconque

Mathieu Huruguen (1)

1 IF - Institut Fourier

We give a definition of spherical homogeneous spaces and their embeddings over an arbitrary field. Given such a homogeneous space X_0, we show that one can associate with each of its embedding a coloured fan which is stable under the action of the Galois group. Then we produce two counter-examples to the converse statement: a Galois stable coloured fan does not necessarily correspond to an embedding of X_0. However, we show that this correspondence works under some additional assumptions.

Domaines: Géométrie algébrique [math.AG]; Théorie des groupes [math.GR]

Mathieu Huruguen. Plongements d'espaces homogènes sphériques sur un corps quelconque. 2009. ⟨hal-00438195v1⟩