Name
Hidekazu Furusho
TITLE:
Motivic Iterated Integrals in Generic Positions
ABSTRACT:
This is a survey on my joint paper [FJ] with Amir Jafari
following [GGL]. We will give a combinatorial framework for
motivic study of iterated integrals on the affine line. We will show
that under a genericity condition these
combinatorial objects give elements,
called motivic iterated integrals, in the motivic Hopf
algebra of the category of mixed Tate motives constructed in [BK].
Using Bloch-Kriz's criteria,
we will show that the Hodge
realization of these elements agrees with the Hodge structure
of iterated integrals
induced from the fundamental torsor of path of punctured affine line.
As an example, our results will produce
algebraic cycles associated with motivic double polylogarithms.
References
[BK]: Bloch, Spencer and Kriz, Igor:
Mixed Tate motives,
Ann. of Math. (2) 140 (1994), no. 3, 557--605.
[FJ]: Furusho, Hidekazu and Jafari, Amir:
Algebraic Cycles and Motivic Generic Iterated Integrals,
Preprint
arXiv:math.NT/0506370.
[GGL]: Gangl, Herbert, Goncharov, Alexander B. and Levin, Andrei:
Multiple polylogarithms, polygons, trees and algebraic cycles,
Preprint
arXive:math.NT/0508066.