W. Dale Brownawell, Chieh-Yu Chang, Matthew A. Papanikolas, Fu-Tsun Wei
Published 2022-03-17Version 1
In this paper we introduce the notion of Shimura's period symbols over function fields in positive characteristic and establish their fundamental properties. We further formulate and prove a function field analogue of Shimura's conjecture on the algebraic independence of period symbols. Our results enable us to verify the algebraic independence of the coordinates of any nonzero period vector of an abelian t-module with complex multiplication whose CM type is non-degenerate and defined over an algebraic function field. This is an extension of Yu's work on Hilbert-Blumenthal t-modules.
Comments: Key words and phrases: period symbols, CM types, t-modules, t-motives
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On the algebraic independence of logarithms of Anderson $t$-modules
Prolongations of t-motives and algebraic independence of periods
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