论文标题
理性椭圆形表面的Weil-Chatelet群
Weil-Chatelet Groups of Rational Elliptic Surfaces
论文作者
论文摘要
我们对$（s，γ）$进行了分类，由理性的椭圆表面$ s $和GALOIS覆盖基础的$γ$组成，这使我们称为$ \ MATHCAL {L} $稳定性。我们解释了如何使用Mordell-Weil晶格的理论来计算Weil-Chatelet组的限制图的内核，以$ \ MATHCAL {L} $ - 稳定对。我们还证明了有关某些对不是$ \ MATHCAL {L} $稳定的某些对的Weil-Chatelet组限制图的注入性的结果。
We classify pairs $(S, γ)$, consisting of a rational elliptic surface $S$ and a Galois cover $γ$ 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.
