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Results tagged with galois-representations
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user 2757
The term Galois representation is frequently used when the G-module is a vector space over a field or a free module over a ring, but can also be used as a synonym for G-module. The study of Galois modules for extensions of local or global fields is an important tool in number theory.
9
votes
Accepted
Cyclic extensions coming from E[p] \equiv F[p],
The answer is that in fact this construction does not produce cyclic extensions! The problem is that $X_E(p^2) \to X_E(p)$ is not generically Galois; it is so only after extension of the ground field …
- 23.8k
22
votes
Accepted
Images of action of Galois on the Tate module of Elliptic Curve,
Let $\Delta$ be the discriminant of $E$. Then the action of $G_{\mathbf{Q}}$ on $E[2]$ determines the action on $\sqrt{\Delta}$. On the other hand, the action of $G_{\mathbf{Q}}$ on $E[n]$ determine …
- 23.8k