Nadir Hajouji
Published 2020-11-30Version 1
We classify pairs $(S, \gamma)$, consisting of a rational elliptic surface $S$ and a Galois cover $\gamma$ of the base, which satisfy a condition we call $\mathcal{L}$-stability. We explain how to use the theory of Mordell-Weil lattices to compute the kernel of the restriction maps of Weil-Chatelet groups for $\mathcal{L}$-stable pairs. We also prove results about the injectivity of restriction maps of Weil-Chatelet groups for some pairs which are not $\mathcal{L}$-stable.
On the existence of a torsor structure for Galois covers
The fundamental group of Galois cover of the surface ${\mathbb T} \times {\mathbb T}$
The fundamental group of a Galois cover of CP^1 X T
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