相关论文: Mixed motivic sheaves (and weights for them) exist…
We study certain 'weights' for triangulated categories endowed with $t$-structures. Our results axiomatize and describe in detail the relations between the Chow weight structure (introduced in a preceding paper), the (conjectural) motivic…
The main goal of this paper is to define the so-called Chow weight structure for the category of Beilinson motives over any 'reasonable' base scheme $S$ (this is the version of Voevodsky's motives over $S$ defined by Cisinski and Deglise).…
The goal of this paper is to define a certain Chow weight structure for the category of Voevodsky's motivic complexes with integral coefficients (as described by Cisinski and Deglise) over any excellent finite-dimensional separated scheme…
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,…
We study various triangulated motivic categories and introduce a vast family of aisles (these are certain classes of objects) in them. These aisles are defined in terms of the corresponding "motives" (or motivic spectra) of smooth varieties…
We apply Wildeshaus's theory of motivic intermediate extensions to the motivic decomposition conjecture, formulated by Deninger-Murre and Corti-Hanamura. We first obtain a general motivic decomposition for the Chow motive of an arbitrary…
The aim of this work is to construct certain homotopy t-structures on various categories of motivic homotopy theory, extending works of Voevodsky, Morel, D\'eglise and Ayoub. We prove these $t$-structures possess many good properties, some…
In this paper certain Chow weight structures on the "big" triangulated motivic categories $DM_R^{eff}\subset DM_R$ are defined in terms of motives of all smooth varieties over the base field. This definition allows studying basic properties…
We consider proper, algebraic semismall maps f from a complex algebraic manifold X. We show that the topological Decomposition Theorem implies a "motivic" decomposition theorem for the rational algebraic cycles of X and, in the case X is…
We describe certain criteria for a motif $M$ to be $r$-effective, i.e., to belong to the $r$th Tate twist $Obj DM^{eff}_{gm,R}(r)=Obj DM^{eff}_{gm,R} \otimes L^{\otimes r}$ of effective Voevodsky motives (for $r\ge 1$; $R$ is the…
We construct a 'triangulated analogue' of coniveau spectral sequences: the motif of a variety over a countable field is 'decomposed' (in the sense of Postnikov towers) into the twisted (co)motives of its points; this is generalized to…
We study in detail the so-called Chow-weight homology of Voevodsky motivic complexes and relate it to motivic homology. We generalize earlier results and prove that the vanishing of higher motivic homology groups of a motif $M$ implies…
The main goal of this paper is to define a certain Chow weight structure $w_{Chow}$ on the category $DM_c(S)$ of (constructible) $cdh$-motives over an equicharacteristic scheme $S$. In contrast to the previous papers of D. H\'ebert and the…
In this paper we prove that the intersections of the levels of the dimension filtration on Voevodsky's motivic complexes over a field $k$ with the levels of the slice one are "as small as possible", i.e., that $Obj d_{\le m}DM^{eff}_{-,R}…
In this paper, we construct four different theories of integration, two that are for Voevodsky motives, one for mixed $\ell$-adic sheaves, and a fourth theory of integration for rational mixed Hodge structures. We then show that they…
With representation-theoretic applications in mind, we construct a formalism of reduced motives with integral coefficients. These are motivic sheaves from which the higher motivic cohomology of the base scheme has been removed. We show that…
This paper investigates the structure of generic motives and their implications for the motivic cohomology of fields. Originating in Voevodsky's theory of motives and related to Beilinson's vision of a motivic $t$-structure, generic motives…
For any cohomology theory $H$ that can be factorized through (the Morel-Voevodsky's triangulated motivic homotopy category) $SH^{S^1}(k)$ we establish the $SH^{S^1}(k)$-functoriality of coniveau spectral sequences for $H$. We also prove:…
In paper 0704.4003, Bondarko recently defined the notion of weight structure, and proved that the category $\DgM$ of geometrical motives over a perfect field k, as defined and studied by Voevodsky, Suslin and Friedlander, is canonically…
This paper is dedicated to triangulated categories endowed with weight structures (a new notion; D. Pauksztello has independently introduced them as co-t-structures). This axiomatizes the properties of stupid truncations of complexes in…