• Lenny Taelman

    University of Amsterdam, Netherlands
1-$t$-Motifs cover
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We show that the module of rational points on an abelian tt\dash module EE is canonically isomorphic with the module Ext1(ME,K[t])\mathrm {Ext}^1(M_E, K[t]) of extensions of the trivial tt-motif K[t]K[t] by the tt-motif MEM_E associated with EE. This generalizes prior results of Anderson and Thakur, Papanikolas and Ramachandran, and Woo.

In case EE 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.