Marc Hoyois's user avatar
Marc Hoyois's user avatar
Marc Hoyois's user avatar
Marc Hoyois
  • Member for 11 years, 1 month
  • Last seen this week
39 votes
Accepted

Is the fundamental group functor a left-adjoint?

25 votes

Why is the motivic category defined over the site of smooth schemes only?

20 votes
Accepted

When is a topological space the homotopy colimit of an open covering?

19 votes
Accepted

Which limits commute with filtered colimits in the category of sets?

18 votes
Accepted

Category of motivic spectra

16 votes

Can we define homotopy groups using Tannakian categories

16 votes
Accepted

$BG$ the stack, $BG$ the simplicial presheaf

15 votes
Accepted

Is the $\infty$-topos $Sh(X)$ hypercomplete whenever $X$ is a CW complex?

15 votes
Accepted

Does the forgetful functor from presentable $\infty$-categories to $\infty$-categories preserve filtered colimits?

14 votes
Accepted

Diffeology as a sheaf on the site of smooth manifolds

14 votes
Accepted

The vanishing of $MGL^{2n+i,n}(X)$; do spectra of smooth projective varieties generate $SH_{l}$?

14 votes
Accepted

Perfect chain complexes

13 votes
Accepted

Realization Functor From $SH$ to Derived Category of $Gal$-Modules

13 votes
Accepted

Sheaves of complexes and complexes of sheaves

13 votes
Accepted

If we replace the spectrally ringed space in the definition of a spectral scheme with an arbitrary infinity-topos, what objects do we get?

13 votes

What is the dual of the stable infinity category of perfect complex on smooth proper variety?

12 votes

Determinantal identities for perfect complexes

12 votes

What's with equivariant homotopy theory over a compact Lie group?

12 votes
Accepted

Are there continua in $\infty$-topoi?

12 votes

What is the negative cyclic homology of a smooth projective variety?

11 votes
Accepted

Derived version of equivalence between motives and representations of Motivic galois groups?

11 votes
Accepted

Is the site of (smooth) manifolds hypercomplete?

11 votes
Accepted

A Kunneth formula for the etale cohomology of the product of ('simple') varieties over not (necessarily) algebraically closed field

10 votes
Accepted

Homotopy left-exactness of a left derived functor

10 votes
Accepted

FIltered colimits of truncated objects in $\infty$-topoi

10 votes
Accepted

When is the pullback in Chow groups defined?

10 votes
Accepted

Is $H_{et}^1(X,F) = H^1(\pi_1^{et}(X), F(\bar{k}))$ true?

10 votes
Accepted

Example of a locally presentable locally cartesian closed category which is not a topos?

10 votes
Accepted

$2$-fiber product is a scheme then map of stacks is representable

10 votes
Accepted

Tensor products of $\mathbb{E}_\infty$-spaces