Serre's conjecture over F_9
数论
2007-05-23 v1 代数几何
摘要
In this paper, we show that an odd Galois representation rhobar: Gal(Qbar/Q) --> GL_2(F_9) satisfying certain local conditions at 3 and 5 is modular. Our main tool is an idea of Taylor, which reduces the problem to that of exhibiting points on a Hilbert modular surface which are defined over a solvable extension of Q, and which satisfy certain reduction properties. As a corollary, we show that Hilbert-Blumenthal abelian surfaces over Q with good ordinary reduction at 3 and 5 are modular.
引用
@article{arxiv.math/0107147,
title = {Serre's conjecture over F_9},
author = {Jordan S. Ellenberg},
journal= {arXiv preprint arXiv:math/0107147},
year = {2007}
}
备注
14 pages