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Marc Hoyois

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earned this badge 35 times.

motivic t-structure and realisations

Awarded May 16 at 21:34

Is $MGL$ an $H\mathbb{Z}$-algebra?

Awarded May 10 at 5:57

Voevodsky's six functor formalism VS Lucas Mann's

Awarded Feb 14 at 6:47

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

Awarded Jan 8 at 18:05

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

Awarded Aug 1, 2022 at 10:12

How duality follows from a six functor formalism

Awarded Jul 7, 2022 at 17:01

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

Awarded Apr 22, 2022 at 19:04

Determinantal identities for perfect complexes

Awarded Apr 13, 2022 at 21:06

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

Awarded Aug 14, 2021 at 8:48

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

Awarded Apr 23, 2021 at 19:26

Sheaves of complexes and complexes of sheaves

Awarded Sep 24, 2020 at 14:26

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

Awarded Jan 30, 2020 at 14:20

Is the site of (smooth) manifolds hypercomplete?

Awarded Oct 18, 2019 at 5:50

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

Awarded Mar 25, 2019 at 21:25

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

Awarded Mar 22, 2019 at 4:45

When is the pullback in Chow groups defined?

Awarded Dec 10, 2018 at 5:25

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

Awarded Oct 19, 2018 at 16:40

Are there continua in $\infty$-topoi?

Awarded Oct 9, 2018 at 12:20

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

Awarded May 26, 2018 at 4:50

Two motivic complexes, compared

Awarded Feb 25, 2018 at 5:52

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

Awarded Feb 16, 2018 at 12:46

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

Awarded Jan 5, 2018 at 18:18

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

Awarded Sep 7, 2017 at 19:38

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

Awarded Jul 19, 2017 at 21:22

Homotopy left-exactness of a left derived functor

Awarded Feb 25, 2017 at 22:50

Perfect chain complexes

Awarded Sep 8, 2016 at 20:49

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

Awarded Mar 29, 2016 at 16:22

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

Awarded Nov 21, 2015 at 15:08

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

Awarded Aug 15, 2015 at 0:02

Category of motivic spectra

Awarded Jan 25, 2015 at 8:34

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

Awarded Nov 23, 2014 at 22:19

Diffeology as a sheaf on the site of smooth manifolds

Awarded Jan 21, 2014 at 18:51

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

Awarded Aug 23, 2013 at 16:41

Can we define homotopy groups using Tannakian categories

Awarded Dec 13, 2012 at 22:50

Is the fundamental group functor a left-adjoint?

Awarded Oct 16, 2012 at 9:35

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