Related papers: On weights for relative motives with integral coef…
We develop the theory of Milnor-Witt motives and motivic cohomology. Compared to Voevodsky's theory of motives and his motivic cohomology, the first difference appears in our definition of Milnor-Witt finite correspondences, where our…
The goal of this paper is to construct trace maps for the six functor formalism of motivic cohomology after Voevodsky, Ayoub, and Cisinski-D\'{e}glise. We also construct an $\infty$-enhancement of such a trace formalism. In the course of…
We prove that under semismall smooth flops, smooth projective varieties have (non-canonically) isomorphic Chow motives with coefficients in any noetherian local ring $\Lambda$ by comparing the pushforward of the constant intersection…
We give a formula for the integral Chow rings of weighted blow-ups. Along the way, we also compute the integral Chow rings of weighted projective stack bundles, a formula for the Gysin homomorphism of a weighted blow-up, and a…
Let $G$ be a reductive algebraic group over a perfect field $k$ and $\cG$ a $G$-bundle over a scheme $X/k$. The main aim of this article is to study the motive associated with $\cG$, inside the Veovodsky Motivic categories. We consider the…
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…
We study the category $DM(S)$ of Beilinson motives (as described by Cisinski and Deglise) over a more or less general base scheme $S$, and establish several nice properties for a version $t_{hom}(S)$ of the perverse homotopy $t$-structure…
For a flat $p$-adic formal family $S$ of log points over a complete discrete valuation ring with perfect residue field of mixed characteristics $(0,p)$ and for a simple normal crossing log scheme $X$ over an exact closed log subscheme of…
We compute the Chow-Witt rings of the classifying spaces for the symplectic and special linear groups. In the structural description we give, contributions from real and complex realization are clearly visible. In particular, the…
We build a unified framework for the study of monodromy operators and weight filtrations of cohomology theories for varieties over a local field. As an application, we give a streamlined definition of Hyodo-Kato cohomology without recourse…
Beginning with the conjecture of Artin and Tate in 1966, there has been a series of successively more general conjectures expressing the special values of the zeta function of an algebraic variety over a finite field in terms of other…
In this paper we discuss a general notion of Weil cohomology theories, both in algebraic geometry and in rigid analytic geometry. We allow our Weil cohomology theories to have coefficients in arbitrary commutative ring spectra. Using the…
We formulate a conjectural hard Lefschetz property for Chow groups, and prove this in some special cases: roughly speaking, for varieties with finite-dimensional motive, and for varieties whose self-product has vanishing middle-dimensional…
The rational points of a smooth curve $X$ over a number field $k$ map to the set of augmentations of the associated motivic algebra. An expectation, related to Kim's conjecture, is that for $X$ hyperbolic, the set of augmentations which…
Motivic cohomology is powerful tool in algebraic geometry with associated realization maps giving important information about the relations between cohomological invariants of schemes and their classifying spaces. The problem of computing…
We give here a simple proof of weighted logarithmic Sobolev inequality, for example for Cauchy type measures, with optimal weight, sharpening results of Bobkov-Ledoux. Some consequences are also discussed.
We describe a new method for constructing a weight structure $w$ on a triangulated category $C$. For a given $C$ and $w$ it allow us to give a fairly comprehensive (and new) description of those triangulated categories consisting of…
Rost defined the Chow group of algebraic cycles with coefficients in a locally constant torsion etale sheaf. We generalize the definition to allow non-torsion coefficients. Chow groups with twisted coefficients are related to Serre's notion…
We show that $\kgl$-linear cohomology theories over an affine Dedekind scheme $S$ admit a canonical weight filtration on resolvable motives without inverting residual characteristics. Combined with upcoming work of Annala--Hoyois--Iwasa,…
For every smooth and separated Deligne-Mumford stack $F$, we associate a motive $M(F)$ in Voevodsky's category of mixed motives with rational coefficients $\mathbf{DM}^{\eff}(k,\mathbb{Q})$. When $F$ is proper over a field of characteristic…