English

Inverse Galois problem for ordinary curves

Algebraic Geometry 2017-12-20 v2 Number Theory

Abstract

We consider the inverse Galois problem over function fields of positive characteristic p, for example, the inverse Galois problem over the projective line. We describe a method to construct certain Galois covers of the projective line and other curves, which are ordinary in the sense that their Jacobian has maximal p-torsion. We do this by constructing Galois covers of ordinary semi-stable curves, and then deforming them into smooth Galois covers.

Keywords

Cite

@article{arxiv.1704.07608,
  title  = {Inverse Galois problem for ordinary curves},
  author = {Raymond van Bommel},
  journal= {arXiv preprint arXiv:1704.07608},
  year   = {2017}
}

Comments

correction of a few small errors, improvements made in presentation, comments are still welcome!

R2 v1 2026-06-22T19:27:00.340Z