All Questions
Tagged with motives triangulated-categories
10 questions
4
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0
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198
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The importance of the Balmer spectrum
Why are Balmer spectra important? Can someone give examples of reconstruction a category by its spectrum (in some sense)?
It would also be interesting to see applications of Balmer spectra to the ...
- 87
3
votes
0
answers
186
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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
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342
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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
709
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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
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0
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81
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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
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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
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140
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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
4
votes
0
answers
513
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Good morphisms of distinguished triangles: can Neeman's method be applied to the motivic stable homotopy category?
It is well known that non-uniqueness of a cone for a morphism in a triangulated category $C$ makes constructing exact functors (of triangulated categories) a difficult task. In section 3 of his "Some ...
- 16.9k
2
votes
0
answers
146
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On 'graded polarizable' triangulated categories; are there any mixed Galois module analogues known? Also on mixed realizations
There is a construction by Beilinson (in section 3 of "Notes on absolute Hodge cohomology") of the derived category of graded polarizable mixed Hodge complexes; he also proved that this category is ...
- 16.9k
30
votes
3
answers
4k
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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