论文标题
Galois部分和$ p $ - 添加期映射
Galois sections and $p$-adic period mappings
论文作者
论文摘要
令$ k $为一个不包含CM子字段的数字字段。对于任何平滑的投射曲线$ y/k $属$ \ geq2 $，我们证明了Grothendieck部分的“ Selmer”部分的图像在$ k_v $ rational-rational-rational-rational-rational-points $ y（k_v）$中是每个有限的plote $ v $的有限的。这提供了对Grothendieck部分猜想的预测的无条件验证。在证明我们的主要结果的过程中，我们还完善并扩展了劳伦斯和Venkatesh的方法，对显式计算产生了潜在的后果。
Let $K$ be a number field not containing a CM subfield. For any smooth projective curve $Y/K$ of genus $\geq2$, we prove that the image of the "Selmer" part of Grothendieck's section set inside the $K_v$-rational points $Y(K_v)$ is finite for every finite place $v$. This gives an unconditional verification of a prediction of Grothendieck's section conjecture. In the process of proving our main result, we also refine and extend the method of Lawrence and Venkatesh, with potential consequences for explicit computations.
