Variétés homogènes sous $\PGL_n$

Details Variétés homogènes sous $\PGL_n$ Variétés homogènes sous $\PGL_n$

2008-01-24

arxiv.org/abs/0801.3811v1

Mathematics

Algebraic Geometry

35 pages

Scientific paper

Let $A$ be an Azumaya algebra over a field. If $G$ is the group of automorphisms of $A$ and $X$ denotes a projective homogeneous variety under $G$, we construct in a very explicit way and under suitable hypotheses a bundle $\mathcal{V}$ on $S$, where $S$ is a (generalized) Severi-Brauer variety associated to $A$, and a canonical isomorphism between $X$ and a flag bundle on $\mathcal{V}$. This allows to explicitely compute Chow groups of $X$ in terms of the Chow groups of $S$.

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