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

TL;DR

This paper explores the analogy between Anderson T-motives and abelian varieties with MIQF, leading to new descriptions of these varieties and constructions of their exterior powers, enhancing understanding of their structure.

Contribution

It provides a novel description of abelian varieties with MIQF via lattices and constructs exterior powers for cases where n=1, based on the analogy with Anderson T-motives.

Findings

Described abelian varieties with MIQF using lattice theory.

Constructed exterior powers of abelian varieties with MIQF for n=1.

Established new links between Anderson T-motives and abelian varieties.

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 $n=1$.