Galois 表示的半单化比较
数论
2019-05-28 v5 表示论
摘要
设 G 为全局域的绝对 Galois 群。设 r1 与 r2 为 G 的两个 p-进有限维表示。则存在有限个素数 q，使得若 r1(Frob_q) 与 r2(Frob_q) 的特征多项式相等，则 r1 与 r2 具有同构的半单化，从而具有相同的 L-函数。我们给出一种基于表示的分歧与维数来计算充分素数表的方法。随后我们将该结果应用于 B. van Geemen 与 J. Top 的一篇文章，其中他们描述了两个表示并猜想它们具有同构的半单化。
引用
@article{arxiv.math/0506053,
title = {Comparison of semi-simplifications of Galois representations},
author = {Loic Grenie},
journal= {arXiv preprint arXiv:math/0506053},
year = {2019}
}
备注
12 pages The fifth version includes further corrections from the referee plus a correction of Proposition 14. The fourth version includes corrections suggested by the referee. It also eliminates the corrections made in second version. The third version corrects a stupid typo. The second version corrects an error in the first one: I had thought that the traces of the representations were enough but I was wrong, I need the characteristic polynomials of one generator per cyclic subgroup