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Results tagged with local-fields
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user 5015
2
votes
Why is the norm map dual to restriction under Tate local duality?
If $m$ is an integer coprime to the characteristic of $k$, then the pairing between $A^t(K)/m A^t(K)$ and the $m$-torsion part of $H^1(K,A)$ is compatible with the cup pairing
$$H^1(K,A^t[m]) \times …
- 8,945
1
vote
Accepted
isogenies between elliptic curves with multiplicative reduction
I believe this is the answer in the split case: Let $E$ be the Tate curve with parameter $q$. Let $n>1$. We look for isogenies with cyclic kernel of order $n$. We may suppose that $n$ is prime.
Firs …
- 8,945
5
votes
Possible $p$-torsion subgroup of $E(\mathbb{Q}_p)$, and if there is a theorem to say which c...
If $p$ is odd then $E(\mathbb{Q}_p)[p]$ is either trivial or one copy of $\mathbb{Z}/p\mathbb{Z}$ and that will be all of the $p$-primary torsion. For $p=2$, all of $E[2]$ can be defined over $\mathbb …
- 8,945
2
votes
Vanishing of the degree 2 cohomology of a p-adic field with coefficients Q/Z and action of t...
I don't think the action of Frobenius $\phi$ is trivial. The inf-res five term exact sequence reduces to a short exact sequence
$$ 0\to \operatorname{Hom}\bigl(G/I, \mathbb{Q}/\mathbb{Z}\bigr)\to \ope …
- 8,945