Lenny TaelmanUniversity of Amsterdam, Netherlands
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We show that the module of rational points on an abelian \dash module is canonically isomorphic with the module of extensions of the trivial -motif by the -motif associated with . This generalizes prior results of Anderson and Thakur, Papanikolas and Ramachandran, and Woo.
In case is uniformizable 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.