Related papers: Motives over simplicial schemes

We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As a result, we obtain a categorical…

We introduce the notion of Artin motives and cohomological motives over a scheme X. Given a cohomological motive M over X, we construct its punctual weight zero part $\omega^0_X(M)$ as the universal Artin motive mapping to M. We use this to…

For smooth linear group schemes over $\bbZ$ we give a cohomological interpretation of the local Tamagawa measures as cohomological periods. This is in the spirit of the Tamagawa measures for motives defined by Bloch and Kato. We show that…

In [1] we introduced the concept of structured space, which is a topological space that locally resembles some algebraic structures. In [2] we proceeded the study of these spaces, developing two cohomology theories. The aim of this paper is…

A kind of motivic algebra of spectral categories and modules over them is developed to introduce K-motives of algebraic varieties. As an application, bivariant algebraic K-theory as well as bivariant motivic kohomology groups are defined…

We introduce a notion of gluability for poset-indexed Bridgeland slicings on triangulated categories and show how a gluing abelian slicing on the heart of a bounded $t$-structure naturally induces a family of perverse $t$-structures. Our…

We study, in the context of Voevodsky's triangulated category of motives, several adequate equivalence relations (in the sense of Samuel) on the graded Chow ring $CH^\ast (X\times Y)$ for $X$, $Y$ smooth projective varieties over a field.

In this note we relate three topics for arithmetic schemes: a general duality for \'etale constructible torsion sheaves, an \'etale homology theory, and a Gersten-Bloch-Ogus-Kato complex. The results in this paper have been used in other…

In this paper, we present a general approach to establish motivic cohomology and build part of its six operations formalism. Applying this together with symplectic orientation on MW-motivic cohomology, we discuss the embedding theorem of…

We define a category of motives for semi-algebraic spaces and show that it is trivial. This implies that there is no good extension of algebraic de Rham cohomology to semi-algebraic spaces compatible with the period isomorphism.

We prove a canonical Kuenneth decomposition of the relative motive with rational coefficients of a smooth commutative group scheme over a noetherian finite dimensional base. This paper is a follow-up of "On the motive of a commutative…

We prove that etale morphisms of schemes yield separable extensions of derived categories. We then generalize the Neeman-Thomason Localization Theorem to separable extensions of triangulated categories.

In this paper, we study a Gysin triangle in the category of motives with modulus. We can understand this Gysin triangle as a motivic lift of the Gysin triangle of log-crystalline cohomology due to Nakkajima and Shiho. After that we compare…

We survey some methods developed in a series of papers, for classifying localising subcategories of tensor triangulated categories. We illustrate these methods by proving a new theorem, providing such a classification in the case of the…

These lecture notes cover four topics. There is a proof of the fact that the functors represented by the motivic Eilenberg-Maclane spaces on the motivic homotopy category coincide with the motivic cohomology defined in terms of the motivic…

In 1986, Kato set up a framework of conjectures relating (higher) $0$-cycles and \'etale cohomology for smooth projective schemes over finite fields or rings of integers in local fields through the homology of so-called Kato complexes. In…

We study the classification of submodules of module categories over monoidal categories, extending ideas of Coulembier on the classification of tensor ideals in monoidal categories. We develop a framework that applies to module categories…

We propose a new look on triangulated categories, which is based on the second Hochschild cohomology.

A phantom category is an admissible subcategory with vanishing Grothendieck group of the bounded derived category of coherent sheaves on a smooth projective variety. The goal of this paper is to study the abstract situation when such a…

We first recall the construction of the Chow motive modelling intersection cohomology of a proper surface and study its fundamental properties. Using Voevodsky's category of effective geometrical motives, we then study the motive of the…