Arithmetic statistics of Selmer groups with a Galois action

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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.