655 citations · 1.7k across the 34 of their papers we have counts for
40 papers
Spectral description of non-commutative local systems on surfaces and non-commutative cluster varieties
Alexander Goncharov, Maxim Kontsevich
Let R be a non-commutative field. We prove that generic triples of flags in an m-dimensional R-vector space are described by flat R-line bundles on the honeycomb graph with (m-1)(m…
Cluster construction of the second motivic Chern class
Alexander B. Goncharov, Olexii Kislinskyi
Let G be a split, simple, simply connected, algebraic group over Q. The degree 4, weight 2 motivic cohomology group of the classifying space BG of G is identified with Z. We constr…
Motivic fundamental group of and modular manifolds
Alexander B. Goncharov
We investigate geometric and combinatorial aspects of the mysterious relationship between the action of the motivic Galois group on the motivic fundamental group of the projective…
Quantum geometry of moduli spaces of local systems and representation theory
Alexander Goncharov, Linhui Shen
Let G be a split semi-simple adjoint group, and S a colored decorated surface, given by an oriented surface with punctures, special boundary points, and a specified collection of b…
Motivic correlators, cluster varieties and Zagier's conjecture on zeta(F,4)
Alexander B. Goncharov, Daniil Rudenko
We prove Zagier's conjecture on the value at s=4 of the Dedekind zeta-function of a number field F. For any field F, we define a map from the appropriate pieces of algebraic K-theo…
The Galois group of the category of mixed Hodge-Tate structures
Alexander Goncharov, Guangyu Zhu
The category of rational mixed Hodge-Tate structures is a mixed Tate category. So thanks to the Tannakian formalism, it is equivalent to the category of finite dimensional graded c…