Selmer groups of abelian varieties in extensions of function fields

Details Selmer groups of abelian varieties in extensions of function fields Selmer groups of abelian varieties in extensions of function fields

2006-01-24

arxiv.org/abs/math/0601580v3

Mathematics

Number Theory

final version, to appear in Mathematische Zeitschrift

Scientific paper

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 \'etale cover defined over $k$ with function field $K':=k(\cac')$. Let $(\tau',B')$ 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-N\'eron} group $A(K')/\tau'B'(k)$. 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-N\'eron} group of $A$ to be uniformly bounded along the tower.

Affiliated with

Also associated with

No associations

Rating

Selmer groups of abelian varieties in extensions of function fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Selmer groups of abelian varieties in extensions of function fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Selmer groups of abelian varieties in extensions of function fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-550954