Mathematics – Number Theory
Scientific paper
2003-02-17
Bulletin de la Soci\'et\'e Math\'ematiques de France 133 (2005), 275-295
Mathematics
Number Theory
18 pages, corrected final version, to appear Bulletin de la Societe Mathematique de France
Scientific paper
On the rank of Jacobians over function fields.} Let $f:\mathcal{X}\to C$ be a projective surface fibered over a curve and defined over a number field $k$. We give an interpretation of the rank of the Mordell-Weil group over $k(C)$ of the jacobian of the generic fibre (modulo the constant part) in terms of average of the traces of Frobenius on the fibers of $f$. The results also give a reinterpretation of the Tate conjecture for the surface $\mathcal{X}$ and generalizes results of Nagao, Rosen-Silverman and Wazir.
Hindry Marc
Pacheco Amilcar
No associations
LandOfFree
Sur le rang des Jacobiennes sur un corps de fonctions 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 Sur le rang des Jacobiennes sur un corps de fonctions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sur le rang des Jacobiennes sur un corps de fonctions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-381488