Search Results

With rational coefficients these two categories are 'almost isomorphic'; this was announced by F. Morel.

My impression is that Adams operations are "well known" to act coherently on all levels of the weight spectral sequence for K-theory (of smooth varieties); probably, this fact was established by Gill …

Let $S$ be a (motivic symmetric) ring spectrum (more generally, one can possibly consider a commutative ring object in any symmetric stable model category); let $R$ be an associative commutative unit …

This is actually an answer to a question you did not ask; sorry. The corresponding diagram $T\wedge T\to T\wedge T$ neither commutes nor anticommutes. An observation of Morel (that was studied in det …

I know of two related applications. For any cohomology theory that factorizes through $H_{A^1}(k)$ one has a certain Gysin long exact sequence $\dots \to H^i(X-Z)\to H^i(X)\to H^i(N_{Z/X}/N_{Z/X}\se …

I will sketch a proof. It suffices to prove that there are only zero morphisms from $M_{\text{gm}}(X)(1)$ into $\mathbb{Z}[q]$ for any smooth $X$ and $q\in \mathbb{Z}$. The latter statement easily f …

As the discussion here Is singular cohomology representable by a (Voevodsky's) motivic complex? shows, the singular cohomology of (smooth) complex varieties is represented by a motivic complex (and al …

The motivic $S^1$-stable homotopy category $SH^{S^1}(k)$ (where $k$ is a field that is often assumed to be perfect; yet one can probably take quite general base schemes here) is "intermediate" betwee …

I will try to give some answers. Voevodsky proved that there could be no 'reasonable' motivic $t$-structure for motives with INTEGRAL coefficients (over a non-algebraically closed field); note that t …

It was proved by Riou in Appendix B of http://arxiv.org/abs/1311.2159 that the spectra of smooth projective varieties do (compactly) generate $SH(k)_{\mathbb{Z}_{(l)}}$ for any $l$ distinct from $\ope …

Theorem 1.2 of the paper "The motivic Hopf map solves the homotopy limit problem for K-theory" (see https://elibm.org/article/10011880) says that (under certain assumptions on the base field) the homo …

Morel has defined the motivic Hopf map $\eta$ (in the motivic stable homotopy category $SH(k)$). I suspect that the following facts are valid for it and its topological "cousin"; please correct me if …

I have two questions related to the stable motivic homotopy categories of Morel-Voevodsky. The first is probably simple; I wonder what is known on the second one. For the algebraic cobordism theory …

I would like to have some sort of transfers in motivic stable homotopy categories in order to adapt Voevodsky's split standard triple argument to cohomology theories that can be factorized through the …

It seems that for the injective model structures for the categories simplicial presheaves and simplicial Nisnevich sheaves (on the category of smooth varieties over a perfect field $k$) there exist co …