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Mirela Ciperiani; Jakob Stix
Galois sections for abelian varieties over number fields
Journal de théorie des nombres de Bordeaux, 27 no. 1 (2015), p. 47-52, doi: 10.5802/jtnb.892
Article PDF | Reviews MR 3346963
Class. Math.: 11G10, 11S25

Résumé - Abstract

For an abelian variety $A$ over a number field $k$, we discuss the space of sections of its fundamental group extension $\pi _1(A/k)$. By analyzing the maximal divisible subgroup of $\operatorname{H}^1(k,A)$ we show that the space of sections of $\pi _1(A/k)$ contains a copy of $\hat{{\mathbb{Z}}}^{[k:{\mathbb{Q}}] \cdot \dim (A)}$ and is never in bijection with $A(k)$. This is essentially a result about the structure of $\operatorname{H}^1(k,\operatorname{T}_\ell (A))$.

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