Genus one curves and Brauer-Severi varieties
Algebraic Geometry
2012-07-23 v1 Number Theory
Abstract
Let K be a field. Let A be a central simple algebra over K and let X be the associated Brauer-Severi variety over K. It has recently been asked if there exists a genus 1 curve C over K such that K(C) splits A. In other words, is there a genus one curve C over K with a morphism to X? In this short note, we explicitly construct such a curve in the case where X has dimension at most 4 (equivalently, when A has degree at most 5).
Keywords
Cite
@article{arxiv.1207.4810,
title = {Genus one curves and Brauer-Severi varieties},
author = {Aise Johan de Jong and Wei Ho},
journal= {arXiv preprint arXiv:1207.4810},
year = {2012}
}
Comments
comments welcome