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.