Arithmetic of the [19,1,1,1,1,1] fibration
代数几何
2007-05-23 v1 数论
摘要
This paper studies the arithmetic of the extremal elliptic K3 surface with configuration of singular fibres [19,1,1,1,1,1]. We give a model over Q such that the Neron Severi group is generated by divisors over Q, and we describe the local Hasse-Weil zeta-functions in terms of a modular form of weight 3. Furthermore we verify the Tate conjecture for the reduction at 3 and comment on a conjecture of T. Shioda concerning the similarity of the lattice of transcendental cycles and a lattice resulting from supersingular reduction.
引用
@article{arxiv.math/0510063,
title = {Arithmetic of the [19,1,1,1,1,1] fibration},
author = {Matthias Schuett and Jaap Top},
journal= {arXiv preprint arXiv:math/0510063},
year = {2007}
}
备注
8 pages, plain text