论文标题
过椭圆曲线的期间 - 指数问题
Period -Index problem for hyperelliptic curves
论文作者
论文摘要
让$ c $成为一个平稳的投影曲线，在一个数字$ k $的情况下，具有理性点。我们证明，在$ \ sha（br（c））$ 2转移中的元素的索引和指数重合。 在附录中，等级2稳定矢量束的模态构象构成，具有奇特的决定因素，在光滑的投影性高ellip曲曲线$ c $ c $ g $的$ g $的$ c $中，在任何特征上都不是一个合理点，而不是$（g-1）$（g-1）$的grassmannian-dimentional-dimentional Linear suppace在某些基本locus的基础上，这是一定的基础属于Quad的基础，这是一件成果的基础。 （\ cite {de-ra}）有理由。我们建立了这种同构的扭曲版本，因此我们得出了一个薄弱的HASSE原理，用于平滑的交点$ x $的两个四边形的$ x $ in $ {\ Mathbb p}^5 $在一个数字字段上：如果$ x $在本地包含一行，则$ x $ x $具有$ k $ rational-rational-rational-rational-rational-rational-rational点。
Let $C$ be a smooth projective curve of genus 2 over a number field $k$ with a rational point. We prove that the index and exponent coincide for elements in the 2-torsion of $\Sha(Br(C))$. In the appendix, an isomorphism of the moduli space of rank 2 stable vector bundles with odd determinant on a smooth projective hyperelliptic curve $C$ of genus $g$ with a rational point over any field of characteristic not two with the Grassmannian of $(g-1)$-dimensional linear subspaces in the base locus of a certain pencil of quadrics is established, making a result of (\cite{De-Ra}) rational. We establish a twisted version of this isomorphism and we derive as a consequence a weak Hasse principle for the smooth intersection $X$ of two quadrics in ${\mathbb P}^5$ over a number field: if $X$ contains a line locally, then $X$ has a $k$-rational point.
