Arithmetic statistics of Selmer groups with a Galois action

设E是定义在数域K上的椭圆曲线，L/K是群G的有限伽罗瓦扩张，p是除G阶的素数。这个项目确定了p-Selmer群的可能结构是一个由G作用的群。对于固定的L，人们可以问当E变化时，每个结构出现的频率是多少。对于固定的E和G，人们可以问，随着L的变化，某个模块出现的频率有多高。这些方法涉及Galois上同调、积分表示理论和数几何。

Let E be an elliptic curve defined over a number field K and let L/K be a finite Galois extension with group G. Let p be a prime dividing the order of G. This project determines the possible structures of the p-Selmer group as a group with an action by G. For a fixed L, one can ask how frequent each of them appears as E varies. For a fixed E and G, one can ask how frequent a certain module appears as L varies. The methods involve Galois cohomology, integral representation theory and the geometry of numbers.