On Davenport-Stothers inequalities and elliptic surfaces in positive characteristic
Number Theory
2009-09-07 v3 Algebraic Geometry
Abstract
We show that the Davenport-Stothers inequality from characteristic 0 fails in any characteristic p>3. The proof uses elliptic surfaces over the projective line and inseparable base change. We then present adjusted inequalities. These follow from results of Pesenti-Szpiro. For characteristic 2 and 3, we achieve a similar result in terms of the maximal singular fibres of elliptic surfaces over the projective line. Our ideas are also related to supersingular surfaces (in Shioda's sense).
Keywords
Cite
@article{arxiv.math/0608427,
title = {On Davenport-Stothers inequalities and elliptic surfaces in positive characteristic},
author = {Matthias Schuett and Andreas Schweizer},
journal= {arXiv preprint arXiv:math/0608427},
year = {2009}
}
Comments
24 pages, 1 table; v3: refereed version with minor changes; some typos corrected and section 2 extended