Anderson T-motives are analogs of abelian varieties with multiplication by imaginary quadratic fields

Details Anderson T-motives are analogs of abelian varieties with multiplication by imaginary quadratic fields Anderson T-motives are analogs of abelian varieties with multiplication by imaginary quadratic fields

2009-07-27

arxiv.org/abs/0907.4712v2

Mathematics

Number Theory

11 pages

Scientific paper

An analogy between abelian Anderson T-motives of rank $r$ and dimension $n$, and abelian varieties over $C$ with multiplication by an imaginary quadratic field $K$, of dimension $r$ and of signature $(n, r-n)$, permits us to get two elementary results in the theory of abelian varieties. Firstly, we can associate to this abelian variety a (roughly speaking) $K$-vector space of dimension $r$ in $C^n$. Secondly, if $n=1$ then we can define the $k$-th exterior power of these abelian varieties. Probably this analogy will be a source of more results. For example, we discuss a possibility of finding of analogs of abelian Anderson T-motives whose nilpotent operator $N$ is not 0.

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