相关论文: Smooth weight structures and birationality filtrat…

We develop birational versions of Voevodsky's triangulated categories of motives over a field, and relate them with the pure birational motives studied in arXiv:0902.4902 [math.AG]. We also get an interpretation of unramified cohomology in…

Using the trivial fiber topology we describe motivic $\infty$-loop spaces and fibrant replacements in the motivic stable homotopy category $\mathbf{SH}_{\mathbb{A}^1,\mathrm{Nis}}(B)$ defined over one-dimensional base schemes $B$.

In this paper we define the triangulated category of motives over a simplicial scheme. The morphisms between the Tate objects in this category compute the motivic cohomology of the underlying scheme. In the last section we consider the…

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…

In this paper we suggest a definition for the category of mixed motives generated by the motive h^1(E) for E an elliptic curve without complex multiplication. We then compute the cohomology of this category. Modulo a strengthening of the…

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 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…

We give a condition which characterises those weight structures on a derived category which come from a Thomason filtration on the underlying scheme. Weight structures satisfying our condition will be called $\otimes ^c$-weight structures.…

The main result of this paper is a computation of the motivic cohomology of varieties of n \times m-matrices of of rank m, including both the ring structure and the action of the reduced power operations. The argument proceeds by a…

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…

Considering a (co)homology theory $\mathbb{T}$ on a base category $\mathcal{C}$ as a fragment of a first-order logical theory we here construct an abelian category $\mathcal{A}[\mathbb{T}]$ which is universal with respect to models of…

The de Rham stack construction of Simpson shows that D-modules are quasicoherent sheaves on a modified geometry. Drinfeld furthermore introduced the ring stack perspective (aka transmutation), which asserts that a coefficient theory is…

For a cellular variety $X$ over a field $k$ of characteristic 0 and an algebraic oriented cohomology theory $\hh$ of Levine-Morel we construct a filtration on the cohomology ring $\hh(X)$ such that the associated graded ring is isomorphic…

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…

This book discusses the construction of triangulated categories of mixed motives over a noetherian scheme of finite dimension, extending Voevodsky's definition of motives over a field. In particular, it is shown that motives with rational…

This paper studies Artin-Tate motives over number rings. As a subcategory of geometric motives, the triangulated category of Artin-Tate motives DATM(S) is generated by motives of schemes that are finite over the base S. After establishing…

We survey over some recent applications of motivic homotopy theory in the definition and the study of $p$-adic cohomology theories. In particular, we revisit the proof of the $p$-adic weight-monodromy conjecture for smooth projective…

Let $S$ and $T$ be smooth projective varieties over an algebraically closed field. Suppose that $S$ is a surface admitting a decomposition of the diagonal. We show that, away from the characteristic of $k$, if an algebraic correspondence $T…

In this paper we explore the isotropic stable motivic homotopy category constructed from the usual stable motivic homotopy category, following the work of Vishik on isotropic motives (see [29]), by killing anisotropic varieties. In…

In this master thesis, we extend results from classical simple homotopy theory to the world of stratified homotopy theory. To obtain a well-established framework to work in, we prove a series of results on two model categories of simplicial…