Construction of Hurwitz Spaces and Application to the Regular Inverse Problem
Number Theory
2014-09-30 v3
Abstract
The author give a simple construction of Hurwitz spaces which is defined by Fried and Volklein, and generalize Hurwitz spaces. As a consequence of this construction, the author prove the regularities of the groups PSO^+_{n}(\mathbb F_{p^m}) if p is an odd prime which congruentes with 7 modulo 12, n is an even positive integer grater than 11 and m=1 or p is an odd prime which congruentes with 7 modulo 12, \varphi (p^m-1)/2+1\eqiv n/2 (\mod 2), p^m\equiv 3(\mod 4) and n>\max\{\varphi(p^m-1),7\}.
Cite
@article{arxiv.1201.1391,
title = {Construction of Hurwitz Spaces and Application to the Regular Inverse Problem},
author = {Kenji Sakugawa},
journal= {arXiv preprint arXiv:1201.1391},
year = {2014}
}
Comments
This paper has been withdrawn by the author due to a crucial error in the proof of Theorem 3.15