Selmer groups of abelian varieties in extensions of function fields
| dc.creator | Pacheco, Amilcar | |
| dc.date | 2006-01-24 | |
| dc.date | 2008-03-17 | |
| dc.date.accessioned | 2026-07-07T09:26:56Z | |
| dc.date.available | 2026-07-07T09:26:56Z | |
| dc.description | Let $k$ be a field of characteristic $q$, $\cac$ a smooth geometrically connected curve defined over $k$ with function field $K:=k(\cac)$. Let $A/K$ be a non constant abelian variety defined over $K$ of dimension $d$. We assume that $q=0$ or $>2d+1$. Let $p\ne q$ be a prime number and $\cac'\to\cac$ a finite geometrically \textsc{Galois} and étale cover defined over $k$ with function field $K':=k(\cac')$. Let $(τ',B')$ be the $K'/k$-trace of $A/K$. We give an upper bound for the $\bbz_p$-corank of the \textsc{Selmer} group $\text{Sel}_p(A\times_KK')$, defined in terms of the $p$-descent map. As a consequence, we get an upper bound for the $\bbz$-rank of the \textsc{Lang-Néron} group $A(K')/τ'B'(k)$. In the case of a geometric tower of curves whose \textsc{Galois} group is isomorphic to $\bbz_p$, we give sufficient conditions for the \textsc{Lang-Néron} group of $A$ to be uniformly bounded along the tower. | |
| dc.description | final version, to appear in Mathematische Zeitschrift | |
| dc.identifier | https://arxiv.org/abs/math/0601580 | |
| dc.identifier | http://arxiv.org/abs/math/0601580 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156926 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | Selmer groups of abelian varieties in extensions of function fields | |
| dc.type | text |