Corpus ID: 18030832

Selmer groups as flat cohomology groups

@article{Cesnavicius2013SelmerGA,
  title={Selmer groups as flat cohomology groups},
  author={Kestutis Cesnavicius},
  journal={arXiv: Number Theory},
  year={2013}
}
Given a prime number $p$, Bloch and Kato showed how the $p^\infty$-Selmer group of an abelian variety $A$ over a number field $K$ is determined by the $p$-adic Tate module. In general, the $p^m$-Selmer group $\mathrm{Sel}_{p^m} A$ need not be determined by the mod $p^m$ Galois representation $A[p^m]$; we show, however, that this is the case if $p$ is large enough. More precisely, we exhibit a finite explicit set of rational primes $\Sigma$ depending on $K$ and $A$, such that $\mathrm{Sel}_{p^m… Expand
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References

SHOWING 1-10 OF 92 REFERENCES
Selmer groups and class groups
On the Equation xp + yq = zr: A Survey
Visualizing Elements in the Shafarevich—Tate Group
Class groups and Selmer groups
...
1
2
3
4
5
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