Duality of Anderson T-motives

Abstract

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).

53 pages. Minor corrections

References in corpus (1)

• Artin t-Motifs

Cited by in corpus (4)

• $h^1\ne h_1$ for Anderson t-motives
• Lattice of the dual of an Anderson $t$-motive in terms of a map to a flag variety
• Introduction to Anderson t-motives: a survey
• Lattice map for Anderson T-motives: first approach