1-t-motifs

2009/08/11 by Lenny Taelman, Taelman, Lenny · 1 citation
Mathematics · Physics and Astronomy · #11G09 #Color Science and Applications #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G09

paper · pdf · doi:10.48550/arxiv.0908.1503

(v2: minor changes, added ref. to Woo; v3: corrected Proposition 8, minor changes)

openalex publication_date 2009/08/11 · arxiv created 2010/07/30 · arxiv updated 2010/08/02 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

We show that the module of rational points on an abelian t-module E is canonically isomorphic with the module Ext¹(M_E, K[t]) of extensions of the trivial t-motif K[t] by the t-motif M_E associated with E. This generalizes prior results of Anderson and Thakur, Papanikolas and Ramachandran, and Woo. In case E is uniformizable then we show that this extension module is canonically isomorphic with the corresponding extension module of Pink-Hodge structures. This situation is formally very similar to Deligne's theory of 1-motifs and we have tried to build up the theory in a way that makes this analogy as clear as possible.

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