All Questions
10 questions
1
vote
1
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383
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Grothendieck rings and the Tannakian formalism
I understand that the Tannakian formalism (which I only "know" extremely superficially) is very important for the theory of motives. I guess "the" conjectural category of motives ...
- 4,547
8
votes
1
answer
603
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How much of the category of motives can be recovered from automorphisms of the Betti functor
Say we are working with schemes over a field $k\subset \mathbb{C}.$ A motive in the sense of Voevodsky is a functor $Sch\to D^bVect$ from (an appropriate category of) schemes to the DG category of ...
- 7,952
11
votes
3
answers
1k
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Why linearization leads to arithmetization?
Sorry for this question, but I think it is really important the intuition here.
Motives can be seen as the 'best' way of linearizing the study of schemes, des-composing them into "cohomological atoms"...
- 1,720
10
votes
1
answer
947
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Derived version of equivalence between motives and representations of Motivic galois groups?
A slight variant $\tilde Mot_{num}(k,\mathbb{Q})$ of the category of pure motives $Mot_{num}(k,\mathbb{Q})$ is a Tannakian category equivalent to a category of representations of some algebraic group $...
- 1,720
7
votes
0
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811
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Roadmap to study (Deligne) Algebraic geometry over Tannakian categories
I would like to know the way to proceed in the first lecture of Deligne's Le groupe fondamental de la droite projective moins trois points.
General advices for reading Deligne's paper.
What should I ...
- 1,720
3
votes
1
answer
465
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Relations between Motivic Galois groups and Motivic t-structure?
What are some relations between the existence of Motivic t-structures and Motivic galois groups?
I heard that indeed the existence of the Motivic t-structure implies the isomorphism between Ayoub's ...
- 1,720
13
votes
0
answers
892
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Stack of Tannakian categories? Galois descent?
I'm having trouble finding a reference for something that I'm guessing the experts worked out long ago. Let's take a local or global field $F$ for this post, and fix a separable algebraic closure $\...
- 13.3k
10
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1
answer
2k
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How does the conjectural Langlands group fit into the Tannakian point of view?
I've read that one way to formulate the Langlands program is the following:
Let $\mathcal{L}_ {\mathbb{Q}}$ be the conjectural Langlands group. Then the category of semi-simple (continuous) ...
23
votes
2
answers
2k
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Why would the category of Motives be Tannakian?
After reading the answer to my previous question: What are the different theories that the motivic fundamental group attempts to unify?
I decided to read up on Tannakian formalism.
Given the ...
- 6,348
8
votes
1
answer
985
views
commutativity constraint in Grothendieck's motives
This is a basic question about Grothendieck's conjectural category $M_k$ of pure motives (over a field $k$). This construction first produces a category (the "false category of motives") which need ...
- 3,867