21 citations · 54 across the 7 of their papers we have counts for
9 papers · 1 filter
Moduli spaces of local systems and higher Teichmuller theory
V. V. Fock, A. B. Goncharov
Let G be a split semisimple algebraic group with trivial center. Let S be a compact oriented surface, with or without boundary. We define {\it positive} representations of the fund…
Galois symmetries of fundamental groupoids and noncommutative geometry
A. B. Goncharov
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 grou…
Multiple zeta-motives and moduli spaces M_{0,n}
A. B. Goncharov, Yu. I. Manin
We give a natural construction of unramified over Z framed mixed Tate motives, whose periods are the multiple zeta values. Namely, for each convergent multiple zeta-value we define…
Periods and mixed motives
A. B. Goncharov
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 ro…
Multiple polylogarithms and mixed Tate motives
A. B. Goncharov
We develop the theory of multiple polylogarithms from analytic, Hodge and motivic point of view. Define the category of mixed Tate motives over a ring of integers in a number field…
Geometry of the trilogarithm and the motivic Lie algebra of a field
A. B. Goncharov
We express the Aomoto trilogarithm explicitely via classical trilogarithm and investigate the algebraic-geometric structures behind this: different realuzations of the weight three…