User D.-C. Cisinski

71 votes

What's the "Yoga of Motives"?

answered Oct 24, 2009 at 0:59

35 votes

Grothendieck's Homotopy Hypothesis - Applications and Generalizations

answered Jun 13, 2014 at 22:59

32 votes

Accepted

Is there an additive model of the stable homotopy category?

answered Mar 4, 2010 at 0:55

31 votes

Why is Milnor K-theory not ad hoc?

answered Nov 5, 2009 at 14:53

30 votes

Accepted

Model structure on Simplicial Sets without using topological spaces

answered Nov 15, 2010 at 12:04

30 votes

What is the motivation for infinity category theory?

answered Jul 16, 2023 at 17:47

29 votes

Accepted

Motivic Cohomology vs. Chow for singular varieties?

answered Oct 15, 2010 at 9:50

29 votes

Accepted

Homotopy theory of schemes examples

answered Oct 26, 2009 at 0:51

25 votes

Are non-empty finite sets a Grothendieck test category?

answered Jan 8, 2010 at 10:17

25 votes

Accepted

Shapes for category theory

answered May 1, 2021 at 12:05

24 votes

Formalism of homotopy theory of schemes

answered Oct 26, 2009 at 23:45

23 votes

Accepted

Homotopy types of schemes

answered Oct 11, 2015 at 19:38

21 votes

Accepted

Localizing an arbitrary additive category

answered Oct 29, 2010 at 16:52

20 votes

Accepted

Is the model category of Complete Segal Spaces right proper?

answered Oct 3, 2010 at 22:39

20 votes

Accepted

Non standard (?) model category structure on (co)chain complexes.

answered Oct 19, 2010 at 10:14

20 votes

Accepted

Derivators (in English)

answered Mar 9, 2010 at 10:04

20 votes

Accepted

The Yoneda Lemma for $(\infty,1)$-categories?

answered Dec 26, 2009 at 18:50

20 votes

Accepted

Why is $\mathsf{D}_{qc}(X)$ the right notion, instead of $\mathsf{D}(\mathsf{QCoh}(X))$?

answered Jul 20, 2021 at 12:36

19 votes

Accepted

Do homotopy limits compute limits in the associated quasicategory in the non-combinatorial model category case?

answered Jul 14, 2014 at 22:46

19 votes

Accepted

Is the simplicial completion of a localizer always a bousfield localization of the injective model structure?

answered Jun 25, 2011 at 20:09

18 votes

Accepted

When does direct image with proper support have a right adjoint?

answered Nov 4, 2009 at 21:46

18 votes

Accepted

commutativity constraint in Grothendieck's motives

answered Apr 16, 2011 at 12:41

18 votes

Making the étale topos construction a fully faithful 2-functor from schemes to Grothendieck topoi

answered Jul 5, 2022 at 10:34

17 votes

Accepted

What exactly do the standard conjectures in characteristic zero refer to?

answered Oct 1, 2022 at 9:38

17 votes

Accepted

What's motivic about $\mathbb{A}^1$-homotopy theory? What's motivic about correspondences?

answered Apr 3, 2021 at 13:15

17 votes

Accepted

Tate twists and cohomology of $\mathbf{P}^1$

answered Dec 5, 2017 at 15:07

16 votes

Accepted

Why $K(X) \longrightarrow G (X)$ is a Poincaré duality for K-theory?

answered Nov 19, 2018 at 11:30

16 votes

Accepted

Finiteness conditions on simplicial sheaves/presheaves

answered Oct 23, 2009 at 3:30

15 votes

Accepted

Which motivic spectra are dualizable?

answered Jul 5, 2018 at 11:29

15 votes

Cofinality for coends?

answered Mar 2, 2020 at 10:44

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93 Answers

What's the "Yoga of Motives"?

Grothendieck's Homotopy Hypothesis - Applications and Generalizations

Is there an additive model of the stable homotopy category?

Why is Milnor K-theory not ad hoc?

Model structure on Simplicial Sets without using topological spaces

What is the motivation for infinity category theory?

Motivic Cohomology vs. Chow for singular varieties?

Homotopy theory of schemes examples

Are non-empty finite sets a Grothendieck test category?

Shapes for category theory

Formalism of homotopy theory of schemes

Homotopy types of schemes

Localizing an arbitrary additive category

Is the model category of Complete Segal Spaces right proper?

Non standard (?) model category structure on (co)chain complexes.

Derivators (in English)

The Yoneda Lemma for $(\infty,1)$-categories?

Why is $\mathsf{D}_{qc}(X)$ the right notion, instead of $\mathsf{D}(\mathsf{QCoh}(X))$?

Do homotopy limits compute limits in the associated quasicategory in the non-combinatorial model category case?

Is the simplicial completion of a localizer always a bousfield localization of the injective model structure?

When does direct image with proper support have a right adjoint?

commutativity constraint in Grothendieck's motives

Making the étale topos construction a fully faithful 2-functor from schemes to Grothendieck topoi

What exactly do the standard conjectures in characteristic zero refer to?

What's motivic about $\mathbb{A}^1$-homotopy theory? What's motivic about correspondences?

Tate twists and cohomology of $\mathbf{P}^1$

Why $K(X) \longrightarrow G (X)$ is a Poincaré duality for K-theory?

Finiteness conditions on simplicial sheaves/presheaves

Which motivic spectra are dualizable?

Cofinality for coends?