Related papers: Polylogarithm Variations and Motivic Extensions of…

We construct motivic $\ell$-adic representations of $\GQ$ into exceptional groups of type $E_7,E_8$ and $G_2$ whose image is Zariski dense. This answers a question of Serre. The construction is uniform for these groups and uses the…

In this paper we prove that the motivic Eisenstein classes associated to polylogarithms of commutative group schemes can be $p$-adically interpolated in \'etale cohomology. This generalizes results for elliptic curves obtained in our former…

We give necessary conditions for a category fibred in pseudo-abelian additive categories over the classifying topos of a profinite group to be a stack; these conditions are sufficient when the coefficients are $\mathbf{Q}$-linear. This…

Let k be a base field of positive characteristic. Making use of topological periodic cyclic homology, we start by proving that the category of noncommutative numerical motives over k is abelian semi-simple, as conjectured by Kontsevich.…

We give the explicit algorithm computing the motivic generalization of the Poincare series of the plane curve singularity introduced by A. Campillo, F. Delgado and S. Gusein-Zade. It is done in terms of the embedded resolution of the curve.…

The goal of this paper is to give an explicit description of the triangulated categories of Tate and Artin-Tate motives with finite coefficients Z/m over a field K containing a primitive m-root of unity as the derived categories of exact…

Smooth projective $\mathbb{G}_m$-varieties with isolated rational fixed points admit Tate Milnor-Witt motives. Over Euclidean fields, we give a splitting formula of such motives, which reduces the computation of their Chow-Witt groups to…

This is a survey of our results on the relation between perturbative renormalization and motivic Galois theory. The main result is that all quantum field theories share a common universal symmetry realized as a motivic Galois group, whose…

Let M be a 1-motive defined over a field of characteristic 0. To M we can associate its motivic Galois group, G_mot(M), which is the geometrical interpretation of the Munford-Tate group of M. We prove that the unipotent radical of the Lie…

Let $G$ denote a finite group and $\pi: Z \to Y$ a Galois covering of smooth projective curves with Galois group $G$. For every subgroup $H$ of $G$ there is a canonical action of the corresponding Hecke algebra $\mathbb{Q}[H \backslash…

In this article, we propose a way of seeing the noncommutative tori in the category of noncommutative motives. As an algebra, the noncommutative torus is lack the smoothness property required to define a noncomutative motive. Thus, instead…

This is a sequel to our previous paper (joint with Furusho). It will give a more natural framework for constructing elements in the Hopf algebra of framed mixed Tate motives according to Bloch and Kriz. This framework allows us to extend…

We establish the complete classification of Chow motives of projective homogeneous varieties for $p$-inner semi-simple algebraic groups, with coefficients in $\mathbb{Z}/p\mathbb{Z}$. Our results involve a new motivic invariant, the Tate…

In a previous work, the author have built two families of distinguished algebraic cycles in Bloch-Kriz cubical cycle complex over the projective line minus three points. The goal of this paper is to show how these cycles induce well-defined…

We define the logarithmic tautological rings of the moduli spaces of Deligne-Mumford stable curves (together with a set of additive generators lifting the decorated strata classes of the standard tautological rings). While these algebras…

We develop a general theory which enables the computation of the Picard group of a symmetric monoidal triangulated category, equipped with a weight structure, in terms of the Picard group of the associated heart. As an application, we…

The present paper is devoted to the relations between Deligne's conjecture on critical values of motivic $L$-functions and the multiplicative relations between periods of arithmetically normalized automorphic forms on unitary groups. As an…

We show that the level 2 case of the cyclotomic Grothendieck-Teichm\"{u}ller groups introduced by Enriquez coincides with the motivic Galois group of mixed Tate motives over $\mathbb{Z}[1/2]$.

We consider categories of equivariant mixed Tate motives, where equivariant is understood in the sense of Borel. We give the two usual definitions of equivariant motives, via the simplicial Borel construction and via algebraic…

In this article we prove that the numerical Grothendieck group of every smooth proper dg category is invariant under primary field extensions, and also that the mod-n algebraic K-theory of every dg category is invariant under extensions of…