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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.
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
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