## Duality of Anderson T-motives. (arXiv:0711.1928v7 [math.NT] UPDATED)

Let \$M\$ be a T-motive. We introduce the notion of duality for \$M\$. Main results of the paper (we consider uniformizable \$M\$ over \$F_q[T]\$ of rank \$r\$, dimension \$n\$, whose nilpotent operator \$N\$ is 0): 1. Algebraic duality implies analytic duality (Theorem 5). Explicitly, this means that the lattice of the dual of \$M\$ is the dual of the lattice of \$M\$, i.e. the transposed of a Siegel matrix of \$M\$ is a Siegel matrix of the dual of \$M\$. 2. Let \$n=r-1\$. There is a 1 -- 1 correspondence between pure T-motives (all they are uniformizable), and lattices of rank \$r\$ in \$C^n\$ having dual (Corollary 8.4).查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 Let \$M\$ be a T-motive. We introduce the notion of duality for \$M\$. Main results of the paper (we consider uniformizable \$M\$ over \$F_q[T]\$ of rank \$r\$, dimension \$n\$, whose nilpotent operator \$N\$ is 0): 1. Algebraic duality implies analytic duality (Theorem 5). Explicitly, this means that the lattice of the dual of \$M\$ is the dual of the lattice of \$M\$, i.e. the transposed of a Siegel matrix of \$M\$ is a Siegel matrix of the dual of \$M\$. 2. Let \$n=r-1\$. There is a 1 -- 1 correspondence between pure T-motives (all they are uniformizable), and lattices of rank \$r\$ in \$C^n\$ having dual (Corollary 8.4).