Mathematics – Algebraic Geometry
Scientific paper
2002-08-20
Mathematics
Algebraic Geometry
51 pages, The final version to appear in Duke Math. J
Scientific paper
We define motivic iterated integrals on the affine line, and give a simple proof of the formula for the coproduct in the Hopf algebra of they make. We show that it encodes the group law in the automorphism group of certain non-commutative variety. We relate the coproduct with the coproduct in the Hopf algebra of decorated rooted planar trivalent trees - a planar decorated version of the Hopf algebra defined by Connes and Kreimer. As an application we derive explicit formulas for the coproduct in the motivic multiple polylogarithm Hopf algebra. We give a criteria for a motivic iterated integral to be unramified at a prime ideal, and use it to estimate from above the space spanned by the values of iterated integrals. In chapter 7 we discuss some general principles relating Feynman integrals and mixed motives.
No associations
LandOfFree
Galois symmetries of fundamental groupoids and noncommutative geometry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Galois symmetries of fundamental groupoids and noncommutative geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Galois symmetries of fundamental groupoids and noncommutative geometry will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-465611