Let $k$ a field of characteristic zero. Let $X$ be a smooth, projective,
geometrically rational $k$-surface. Let $\mathcal{T}$ be a universal torsor
over $X$ with a $k$-point et $\mathcal{T}^c$ a smooth compactification of
$\mathcal{T}$. There is an open question: is $\mathcal{T}^c$ $k$-birationally
equivalent to a projective space? We know that the unramified cohomology groups
of degree 1 and 2 of $\mathcal{T}$ and $\mathcal{T}^c$ are reduced to their
constant part. For the analogue of the third cohomology groups, we give a
sufficient condition using the Galois structure of the geometrical Picard group
of $X$. This enables us to show that
$H^{3}_{nr}(\mathcal{T}^{c},\mathbb{Q}/\mathbb{Z}(2))/H^3(k,\mathbb{Q}/\mathbb{Z}(2))$
vanishes if $X$ is a generalised Ch\^atelet surface and that this group is
reduced to its $2$-primary part if $X$ is a del Pezzo surface of degree at
least 2.
Comment: 27 page, in French
Degree three unramified cohomology groups and Noether's problem for groups of order 243
