Periods of t-modules as special values - Maurischat, Andreas (Journal of number theory, 2018)
In this article we show that all periods of uniformizable t-modules (resp. their coordinates) can be obtained via specializing a rigid analytic trivialization of a related dual t-motive at t=θ. The proof is even constructive. The central object in the construction is a subset H of the Tate algebra points of E which turns out to be isomorphic to the period lattice of E via kind of generating series in one direction and residues in the other. This isomorphism even holds for arbitrary t-modules E, even non-abelian ones.
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