论文标题
$ p $ - 阿迪亚在曲线上的理性点
A $p$-adic approach to rational points on curves
论文作者
论文摘要
1922年，莫德尔（Mordell）猜想了一个惊人的说法，即对于多项式方程式$ f（x，y）= 0 $，如果一组复杂数字解决方案的拓扑足够复杂，则一组有理数解决方案是有限的。 Faltings在1983年证明了这一点，Vojta在1991年再次证明了这一点，但两者都没有提供证明找到所有理性解决方案的方法，因此寻找其他证据的搜索仍在继续。最近，劳伦斯（Lawrence）和维卡茨（Venkatesh）发现了第三个证据，依靠$ p $ adic aadic galois代表的差异；这是当前博览会的主题。
In 1922, Mordell conjectured the striking statement that for a polynomial equation $f(x,y)=0$, if the topology of the set of complex number solutions is complicated enough, then the set of rational number solutions is finite. This was proved by Faltings in 1983, and again by a different method by Vojta in 1991, but neither proof provided a way to provably find all the rational solutions, so the search for other proofs has continued. Recently, Lawrence and Venkatesh found a third proof, relying on variation in families of $p$-adic Galois representations; this is the subject of the present exposition.
