Anderson t-motives and abelian varieties with MIQF: Results coming from an analogy

Abstract

Analogy between Anderson [Formula: see text]-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 [Formula: see text] and signature [Formula: see text] in terms of ”lattices” of dimension [Formula: see text] in [Formula: see text]; (2) A construction of exterior powers of abelian varieties with MIQF having [Formula: see text].