Periods and mixed motives

By A. Goncharov. 2002

59 citations recorded by the source corpus.

We define motivic multiple polylogarithms and prove the double shuffle relations for them. We use this to study the motivic fundamental group of the multiplicative group - {N-th roots of unity} and relate it to geometry of modular varieties. In particular we get new information about the actionof the Galois group on the pro-l completion of the above fundamental group. This paper is the second part of "Multiple polylogarithms and mixed Tate motives" math.AG/0103059

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0b03d7f86b306a77663b044bd6c391a64bbf1bb6

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In Algebra and Number Theory

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Citations in the corpus

Renormalization of multiple zeta values (2006, methodology): “by a change of variables zi = e rie ,1 ≤ i ≤ k. As is well-known [5, 23 ], the product”
Double shuffle relation for associators (2008, methodology): “When a is of the form (1,1, � � � ,1), the proof is given by the same argument as in [ Go ] lemma 7.9 as follows: By the series shuffle formulae,”
Iterated integrals of modular forms and noncommutative modular symbols (2005, background): “For the harmonic shuffle relations between multiple zeta values, A. Goncharov established this in [ Go6 , Chapter 9] (for convergent integrals), and in [Go6, 7.5] elaborating the last page of [Go4] (for regularized integrals).”
Mixable shuffles, quasi-shuffles and Hopf algebras (2005, background): “For instance, the construction of the stuffle product in [5] follows easily from the construction of free Rota-Baxter algebras in [6], while the generalized shuffle product in [ 19 ] isthe same as the mixable shuffle product in [23, 24].”
FREE ROTA–BAXTER ALGEBRAS AND ROOTED TREES (2005, background): “ne given by Bradley [10] to explicitly describe stuﬄes and q-stuﬄes for multiple zeta values. Furthermore, the mixable shuﬄe product in the construction in [34] appeared also in the work of Goncharov [29] to study motivic shuﬄe relations. In [20], the mixable shuﬄe product is shown to be the same as”