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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
2
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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 …
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 …