Anderson T-motives are analogs of abelian varieties with multiplication by imaginary quadratic fields
Logachev, D.
arXiv, 0907.4712 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2009-07-27
Classification:  Mathematics - Number Theory,  Mathematics - Algebraic Geometry,  11G09, 11G10, 11G15, 14K99 
@article{0907.4712,
     author = {Logachev, D.},
     title = {Anderson T-motives are analogs of abelian varieties with multiplication
  by imaginary quadratic fields},
     journal = {arXiv},
     volume = {2009},
     number = {0},
     year = {2009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0907.4712}
}

Logachev, D. Anderson T-motives are analogs of abelian varieties with multiplication
  by imaginary quadratic fields. arXiv, Tome 2009 (2009) no. 0, . http://gdmltest.u-ga.fr/item/0907.4712/