Martin Orr's Blog

The Faltings height and normed modules

Posted by Martin Orr on Saturday, 31 December 2011 at 15:31

In this post I shall give the definition of the Faltings height of an abelian variety over any number field. Last time we did this over \mathbb{Q} only, and we used two properties of \mathbb{Q}: the integers are a PID and there is only one archimedean place. To do things more generally, we will introduce the technology of normed modules and their degrees.

2 comments Tags abelian-varieties, alg-geom, faltings, maths, number-theory