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Results tagged with algebraic-number-theory
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user 51164
Algebraic number fields, Algebraic integers, Arithmetic Geometry, Elliptic Curves, Function fields, Local fields, Arithmetic groups, Automorphic forms, zeta functions, $L$-functions, Quadratic forms, Quaternion algebras, Homogenous forms, Class groups, Units, Galois theory, Group cohomology, Étale cohomology, Motives, Class field theory, Iwasawa theory, Modular curves, Shimura varieties, Jacobian varieties, Moduli spaces
13
votes
Accepted
Ranks of elliptic curves depend only on the field?
The answer is yes, at least if you assume that Tate-Shafarevich conjecture.
Let $E$ be an elliptic curve over a number field $k$. Under some mild hypothesis (see Corollary 1.10 of http://arxiv.org/ab …
- 9,491
2
votes
Accepted
A question on the injectivity of a canonical map between galois cohomology groups
I believe this map is always injective. Here is a quick argument: first note that $K'$ is normal over $k$ (because it is invariant under any automorphism of the algebraic closure of $k$ which preserve …
- 9,491