Martin Orr's Blog

Dual varieties over general fields

Posted by Martin Orr on Friday, 24 June 2011 at 17:26

Today we will construct dual abelian varieties over number fields. We use the universal property from two posts ago to define dual abelian varieties, then we give a simple construction inspired by the complex case. Proving that this construction satisfies the universal property is harder; in the case of number fields, we will use Galois descent to deduce it from the complex case which we already know analytically.

2 comments Tags abelian-varieties, alg-geom, hodge, maths