Related papers: Complexe de Poids, Dualit\'e et Motifs de Beilinso…

In this paper, we construct a monoidal weight structure on the stable $\infty$-category of rigid analytic motives over a local field $K$ via Galois descent. This extends the weight structure on the full subcategory of rigid analytic motives…

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 construct a functor from the triangulated category of Voevodsky motives to a certain derived category of mixed Hodge structures enriched with integral weight filtration. We use this construction to prove a strong integral version of the…

Grothendieck first defined the notion of a "motif" as a way of finding a universal cohomology theory for algebraic varieties. Although this program has not been realized, Voevodsky has constructed a triangulated category of geometric…

Bondarko's (strong) weight complex functor is a triangulated functor from Voevodsky's triangulated category of motives to the homotopy category of chain complexes of classical Chow motives. Its construction is valid for any dg enhanced…

We define a motive whose realizations afford modular forms (of arbitrary weight) on an indefinite division quaternion algebra. This generalizes work of Iovita--Spiess to odd weights in the spirit of Jordan--Livn\'e. It also generalizes a…

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 develop a theory of completeness for weight structures on stable categories, dual to the theory of complete t-structures. As in the bounded case, we show that complete weight structures are determined by their weight heart, giving rise…

The main goal of this paper is to deduce (from a recent resolution of singularities result of Gabber) the following fact: (effective) Chow motives with $Z[1/p]$-coefficients over a perfect field $k$ of characteristic $p$ generate the…

This paper proves the Beilinson-Soul{\'e} vanishing conjecture for motives attached to the moduli spaces of curves of genus 0 with n marked points. As part of the proof, it is also proved that these motives are mixed Tate. As a consequence…

We define a notion of pseudo-unitarizability for weight modules over a generalized Weyl algebra (of rank one, with commutative coeffiecient ring $R$), which is assumed to carry an involution of the form $X^*=Y$, $R^*\subseteq R$. We prove…

We make explicit Serre's generalization of the Sato-Tate conjecture for motives, by expressing the construction in terms of fiber functors from the motivic category of absolute Hodge cycles into a suitable category of Hodge structures of…

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…

Let $f$ be a cuspidal eigenform of weight two and level $N$, let $p\nmid N$ be a prime at which $f$ is congruent to an Eisenstein series and let $V_f$ denote the $p$-adic Tate module of $f$. Beilinson constructed a class $\kappa_f\in…

The purpose of the present article is to show the multilinearity for symbols in Goodwillie-Lichtenbaum complex in two cases. The first case shown is where the degree is equal to the weight. In this case, the motivic cohomology groups of a…

This paper examines a number of related questions about Euler characteristics and characteristic classes with values in Witt cohomology. We establish a motivic version of the Becker-Gottllieb transfer, generalizing a construction of Hoyois.…

Using techniques due to Dwyer-Greenlees-Iyengar we construct weight structures in triangulated categories generated by compact objects. We apply our result to show that, for a dg category whose homology vanishes in negative degrees and is…

Over a perfect field k, let G be an extension of an abelian variety by the multiplicative group $\G_m$. We compute the motive of G in Voevodsky's category of etale motivic complexes with rational coefficients. The result is a decomposition…

Let $k$ be a field admitting resolution of singularities. We lift a number of motivic measures, such as the Gillet-Soul\'e measure and the compactly supported $\mathbb{A}^1$-Euler characteristic, to derived motivic measures in the sense of…

For $g\ge 2$ and $n\ge 0$, let $\mathcal{H}_{g,n}\subset \mathcal{M}_{g,n}$ denote the complex moduli stack of $n$-marked smooth hyperelliptic curves of genus $g$. A normal crossings compactification of this space is provided by the theory…