All Questions
7 questions
3
votes
0
answers
186
views
Direct images commute with homotopy colimits
In Les six opérations de Grothendieck et le formalisme des cycles évanescents dans le monde motivique (II), Ayoub defined the notion of a stable homotopical algebraic derivators; roughly, for a ...
- 883
4
votes
0
answers
342
views
Voevodsky's motives and Deligne's systems of realizations
$\newcommand{\gm}{\mathrm{gm}}$Let $\mathbf{DM}_{\gm}(\mathbb{Q},\mathbb{Z})$ be Voevodsky's category of geometric motives over $\mathbb{Q}$ with coefficients in $\mathbb{Z}$ (e.g. as on p.124 of ...
- 15.4k
7
votes
1
answer
710
views
A question on Voevodsky´s categories
I want to try to understand the Voevodsky´s big triangulated categories of motives $DM$ and $DM^{eff}$. Unfortunately, I am being not able to find answers to the following, too vague, questions:
1.- ...
- 761
1
vote
0
answers
81
views
When the tensor product of motives that are not $0$-(homotopy)-connective can be $0$-connective?
For $t$ being the homotopy $t$-structure for Voevodsky effective motivic complexes
when $M\otimes N\in DM_{eff}^{t\le -1}$ ensures that either $M$ or $N$ belongs to $DM_{eff}^{t\le -1}$ (so, we use ...
- 16.9k
12
votes
0
answers
1k
views
Use of derivators to the theory of motives?
This is a rather imprecise question but i think this could become a interesting pool of ideas and comments.
The theory of motives has evolved to a complex field of research the moment Voevodsky (and ...
- 1,479
1
vote
0
answers
140
views
The right (not the left 'Suslin complex' one) adjoint to the embedding of $ DM^{eff} $ into $D(ShvTr) $?
Inside the derived category of Nisnevich sheaves with transfers there is the category $DM^{eff} $ of Voevodsky's effective motivic complexes (actually, Voevodsky only considered bounded above ...
- 16.9k
30
votes
3
answers
4k
views
t-structures and higher categories?
I'm curious to find out where the viewpoint of higher categories may be useful so here is a somewhat vague question (which may or may not have a reasonable answer).
Given a triangulated category, one ...
- 23.5k