Periods of $t$-modules as special values

Abstract

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 $t=\theta$. 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.

15 pages; v1->v2: added references; removed condition "abelian" in Section 3; added Section 4 relating H to sigma-invariants of the dual t-motive v2->v3: added bound on the rank of H; final version to appear in Journal of Number Theory

References in corpus (1)

• A rapid introduction to Drinfeld modules, $t$-modules, and $t$-motives

Cited by in corpus (9)

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• Algebraic relations among hyperderivatives of periods and logarithms of Drinfeld modules
• Anderson t-modules with thin t-adic Galois representations
• Taylor coefficients of Anderson generating functions and Drinfeld torsion extensions
• Abelian equals A-finite for Anderson A-modules
• Residue of special functions of Anderson $A$-modules at the characteristic graph