相关论文: Mixed Artin-Tate motives over number rings

In earlier work (arXiv:0801.0261), we gave a definition of an abelian category of motivic (constructible) sheaves over a base in characteristic zero using Nori's method. This category has Hodge and etale realizations, and is stable under…

Small, finite entities are easier and simpler to manipulate than gigantic, infinite ones. Consequently huge chunks of mathematics are devoted to methods reducing the study of big, cumbersome objects to an analysis of their finite building…

We show that a triangulated motivic category admits categorical Thom isomorphisms for vector bundles with an additional structure if and only if the generalized motivic cohomology theory represented by the tensor unit object admits Thom…

In this paper, we show that a map $\delta$ over a triangular ring $\mathcal{T}$ satisfying $\delta(ab+ba)=\delta(a)b+a \tau(b)+\delta(b)a+b\tau(a)$, for all $a,b\in \mathcal{T}$ and for some maps $\tau$ over $\mathcal{T}$ satisfying…

This is a survey of author's results on weight structures and Voevodsky's motives. Weight structures are natural counterparts of t-structures (for triangulated categories) introduced by the author. They allow to construct weight complexes,…

In this paper, we study the combinatorics of a subcomplex of the Bloch-Kriz cycle complex [4] used to construct the category of mixed Tate motives. The algebraic cycles we consider properly contain the subalgebra of cycles that correspond…

We construct abelian categories of integral Nori motivic sheaves over a scheme of characteristic zero. The first step is to study the presentable derived category of Nori motives over a field. Next we construct an algebra in \'etale motives…

For any cohomology theory $H$ that can be factorized through (the Morel-Voevodsky's triangulated motivic homotopy category) $SH^{S^1}(k)$ (or through $SH(k)$) we establish the $SH^{S^1}(k)$-functorialty (resp. $SH(k)$-one) of coniveau…

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…

In this thesis we compare V. Voevodsky's geometric motives to the derived category of M. Nori's abelian category of mixed motives by constructing a triangulated tensor functor between them. It will be compatible with the Betti realizations…

We show that the derived category of perverse Nori motives and mixed Hodge modules are the derived categories of their constructible hearts. This enables us to construct $\infty$-categorical lifts of the six operations and therefore to…

Let $\mathcal{A}$ be an additive category and let $T\colon \mathcal{A}\rightarrow \mathcal{A}$ be an additive functor equipped with a natural transformation $\omega\colon \mathrm{Id}_{\mathcal{A}}\rightarrow T$. We prove that the homotopy…

We construct the reduction of an exact category with a twist functor with respect to an element of its graded center in presence of an exact-conservative forgetful functor annihilating this central element. The procedure allows, e.g., to…

K. Kato has recently defined and studied heights of mixed motives and proposed some interesting questions. In this paper, we relate the study of heights to the study of Tamagawa numbers of motives. We also partially answer one of Kato's…

We study smashing subcategories of a triangulated category with coproducts via silting theory. Our main result states that for derived categories of dg modules over a non-positive differential graded ring, every compactly generated…

The main goal of this paper is to study relative versions of the category of modules over the isotropic motivic Brown-Peterson spectrum, with a particular emphasis on their cellular subcategories. Using techniques developed by Levine, we…

This paper surveys the recent advances concerning the relations between triangulated (or derived) categories and their dg enhancements. We explain when some interesting triangulated categories arising in algebraic geometry have a unique dg…

To any dg-category $T$ (over some base ring $k$), we define a $D^{-}$-stack $\mathcal{M}_{T}$ in the sense of \cite{hagII}, classifying certain $T^{op}$-dg-modules. When $T$ is saturated, $\mathcal{M}_{T}$ classifies compact objects in the…

In this paper we give a construction of phantom categories, i.e. admissible triangulated subcategories in bounded derived categories of coherent sheaves on smooth projective varieties that have trivial Hochschild homology and trivial…

A mixed Weil cohomology with values in an abelian rigid tensor category is a cohomological functor on Voevodsky's category of motives which is satisfying K\"unneth formula and such that its restriction to Chow motives is a Weil cohomology.…