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Abstract: An analogy between abelian Anderson T-motives of rank $r$ and dimension $n$,and abelian varieties over $C$ with multiplication by an imaginary quadraticfield $K$, of dimension $r$ and of signature $n, r-n$, permits us to get twoelementary results in the theory of abelian varieties. Firstly, we canassociate to this abelian variety a roughly speaking $K$-vector space ofdimension $r$ in $C^n$. Secondly, if $n=1$ then we can define the $k$-thexterior power of these abelian varieties. Probably this analogy will be asource of more results. For example, we discuss a possibility of finding ofanalogs of abelian Anderson T-motives whose nilpotent operator $N$ is not 0.



Author: D. Logachev

Source: https://arxiv.org/







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