Related papers: The cdh-local motivic homotopy category

For a quasiprojective variety S, we define a category CHM(S) of pure Chow motives over S. Assuming conjectures of Grothendieck and Murre, we show that the decomposition theorem holds in CHM(S). As a consequence, the intersection complex of…

We develop the categorical algebra of the noncommutative base change of a comodule category by means of a Grothendieck category $\mathfrak S$. We describe when the resulting category of comodules is locally finitely generated, locally…

Let S be a toric algebra over a field K of characteristic 0 and let I be a monomial ideal of S. We show that the local cohomology modules H^i_I(S) are of finite length over the ring of differential operators D(S;K), generalizing the…

We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopenka's principle. We prove that the necessary large-cardinal…

Motivated by applications to the categorical and geometric local Langlands correspondences, we establish an equivalence between the category of filtered $\mathcal{D}$-modules on a smooth stack $X$ and the category of $S^1$-equivariant…

We define the category of \'etale Chow motives as the \'etale analogue of Grothendieck motives and proved that it embeds in $\text{DM}_{\text{\'et}}(k)$. This construction provides a characterization of the generalized Hodge conjecture in…

A procedure for constructing bivariant theories by means of Grothendieck duality is developed. This produces, in particular, a bivariant theory of Hochschild (co)homology on the category of schemes that are flat, separated and essentially…

We give an alternate formulation of pseudo-coherence over an arbitrary derived stack X. The full subcategory of pseudo-coherent objects forms a stable sub-infinity-category of the derived category associated to X. Using relative…

In this work, we show deep connections between Locality Sensitive Hashability and submodular analysis. We show that the LSHablility of the most commonly analyzed set similarities is in one-to-one correspondance with the supermodularity of…

Let k be an algebraically closed field of characteristic zero. Let SH(k) denote the motivic stable homotopy category of T-spectra over k and SH the classical stable homotopy category. Let c:SH -> SH(k) be the functor induced by sending a…

In this work we develop a theory of motives for logarithmic schemes over fields in the sense of Fontaine, Illusie, and Kato. Our construction is based on the notion of finite log correspondences, the dividing Nisnevich topology on log…

This paper continues our study of the sheaf associated to K\"ahler differentials in the cdh-topology and its cousins, in positive characteristic, without assuming resolution of singularities. The picture for the sheaves themselves is now…

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 the present paper, we prove that a locally noetherian superscheme $X^\circledS$ may be reconstructed (up to certain equivalence) category-theoretically from the category of noetherian superschemes over $X^\circledS$. This result is a…

We formalize an abstraction of Grothendieck's philosophy of motives and construct a category of derived motivic spectra in the Segal category $\mathbb{R} \underline{\text{Hom}} ((\text{dSt}_k)^{\text{op}}_{/F}, \text{Top})$ ($\text{dSt}_k$…

We consider the category of comodules over a smash coproduct coalgebra $C\smashco H$. We show that there is a Grothendieck spectral sequence connecting the derived functors of the Hom functors coming from $C\smashco H$-colinear,…

Let X be a Noetherian scheme of finite dimension and denote by rho the (additive inverse of the) morphism in SH(X) from S to Gm corresponding to the unit -1. Here SH(X) denotes the motivic stable homotopy category. We show that the category…

This is an expository paper providing an overview of the unstable motivic homotopy category using the theory of $(\infty,1)$-categories. In this paper, we examine two constructions in the literature and discuss their equivalence.

We prove a duality statement on modules over KH-theory in the stable motivic homotopy category whose dualizing object is given by G-theory, over any quasi-excellent scheme of characteristic zero.

We prove an h-principle with boundary condition for a certain class of topological spaces valued sheaves. The techniques used in the proof come from the study of the homotopy type of the cobordism categories, and they are of simplicial and…