Multizeta shuffle relations for function fields with non rational infinite place

Abstract

In contrast to the ‘universal’ multizeta shuffle relations, when the chosen infinite place of the function field over Fq is rational, we show that in the non-rational case, only certain interesting shuffle relations survive, and the Fq-linear span of the multizeta values does not form an algebra. This is due to the subtle interactions between the larger finite field F∞, the residue field of the completion at infinity where the signs live and Fq, the field of constants where the coefficients live. We study the classification of these special relations which survive.