Points of low height on P 1 over number fields and bounds for torsion in class groups

@inproceedings{Ellenberg2007PointsOL,
  title={Points of low height on P 1 over number fields and bounds for torsion in class groups},
  author={Jordan S. Ellenberg},
  year={2007}
}
Let K be a number field and ` a positive integer. The main theorem of [3] gives an upper bound for the order of the `-torsion subgroup in the ideal class group ClK of K under the Generalized Riemann Hypothesis, which can be made unconditional in certain special cases (e.g. when K/Q is a quadratic extension and ` = 3.) The main idea is to show that there are many ideal classes which are not `-torsion. This is accomplished by showing that there are many ideals I1, I2, . . . , Is of small height… CONTINUE READING