On a problem of Miyaoka
Number Theory
2007-05-23 v2 Algebraic Geometry
Abstract
We give an example of a vector bundle E on a relative curve C --> Spec Z such that the restriction to the generic fiber in characteristic zero is semistable but such that the restriction to positive characteristic p is not strongly semistable for infinitely many prime numbers. Moreover, under the hypothesis that there exist infinitely many Sophie Germain primes, there are also examples such that the density of primes with non strongly semistable reduction is arbitrarily high.
Cite
@article{arxiv.math/0407475,
title = {On a problem of Miyaoka},
author = {Holger Brenner},
journal= {arXiv preprint arXiv:math/0407475},
year = {2007}
}
Comments
New version: minor changes and improvements