An abelian scheme over a scheme 
is a smooth proper group scheme
over 
whose geometric fibers are connected abelian
varieties. The group law is part of the structure and is compatible with base
change. Over the spectrum of a field, an abelian scheme
is an abelian variety.
An abelian variety over a discretely valued field has good reduction when it extends to an abelian scheme over the valuation ring. The special fiber then supplies the reduction used in Milne's rationality conjecture.
