Speaker: Javier Fresan
A construction of the polylogarithm motive
Classical polylogarithms give rise to a variation of mixed Hodge-Tate structures on the projective line minus three points, which is an extension of the symmetric power of the Kummer variation by a trivial variation. By results of Beilinson-Deligne, Huber-Wildeshaus and Ayoub, this polylogarithm variation has a lift to the category of mixed Tate motives, whose existence is proved by computing the corresponding spaces of extensions both in the Hodge and the motivic settings. I will present a joint work with Clément Dupont, in which we construct the polylogarithm motive as an explicit relative cohomology motive.