Ideal classes and abelian varieties over finite fields

This mini-course will be divided in two parts. In the first we will discuss how to compute all ideal classes of a non-maximal order in étale Qalgebras (i.e. products of number fields). In the second part we will introduce abelian varieties over finite fields and we will describe them by mean of a much more concrete category, which, under certain assumptions, can be described in terms of fractional ideals.