Title: Generalized Ihara-Soule characters and relations among their special values at distinct Galois elements
Abstract: Let l be a prime number, let K be a number field, and let X denote the projective line minus three points. The simplest non-trivial part of the Galois action on the pro-l etale fundamental groupoid of X is described by the generalized Ihara-Soule characters introduced by Nakamura and Wojtkowiak, which are l-adic etale analogues of the polylogarithms. A polylogarithm depends on a complex point of X together with a path in X; a generalized Ihara-Soule character likewise depends on a K-rational point and an etale path in X, but it is moreover a function on the absolute Galois group of K. Previous works have established for these characters a variety of functional equations mirroring those of the classical polylogarithms, all of which arise from varying the point and the path. In this talk we will discuss relations among the special values of generalized Ihara-Soule characters obtained by varying not only the K-rational point and the etale path but also the element of the absolute Galois group.