Duality of Anderson T-motives

A. Grishkov, D. Logachev

Published 2007-11-13, updated 2019-02-05Version 7

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).