On some differences between number fields and function fields
Algebraic Geometry
2016-06-22 v1
Abstract
The analogy between the arithmetic of varieties over number fields and the arithmetic of varieties over function fields is a leading theme in arithmetic geometry. This analogy is very powerful but there are some gaps. In this note we will show how the presence of isotrivial varieties over function fields (the analogous of which do not seems to exist over number fields) breaks this analogy. Some counterexamples to a statement similar to Northcott Theorem are proposed. In positive characteristic, some explicit counterexamples to statements similar to Lang and Vojta conjectures are given.
Keywords
Cite
@article{arxiv.1606.06517,
title = {On some differences between number fields and function fields},
author = {Carlo Gasbarri},
journal= {arXiv preprint arXiv:1606.06517},
year = {2016}
}
Comments
To appear in the "Atti del Terzo Incontro Italiano di Teoria dei Numeri - Pisa - Settembre 2015". Comments are welcome