Anderson T-motives and abelian varieties with MIQF: results coming from an analogy

Abstract

Analogy between Anderson T-motives and abelian varieties with multiplication by an imaginary quadratic field (MIQF) is a source of 2 results: 1. A description of abelian varieties with MIQF of dimension $r$ and signature $(n, r-n)$ in terms of "lattices" of dimension $r$ in $\Bbb C^n$; 2. A construction of exterior powers of abelian varieties with MIQF having $n=1$.