18 problems

Comonotone classification conjecture. If $f$ is comonotone, then $N(f)$ is an aisle.

Generalized telescope conjecture. The assertion is exactly the stable telescope conjecture, or equivalently its ideal-theoretic reformulation, with $\mathbf{t}$ a t-structure in…

Let $X$ be a noetherian scheme. A coherent subset of $X$ is a subset of the underlying topological space of the kind appearing in Krause's classification for commutative noetherian…

Antieau–Gepner–Heller's theorem of the heart conjecture. The map

Let $\sC$ be a small stable $\infty$-category equipped with a bounded t-structure. A spectrum is connective when its negative homotopy groups vanish. Antieau–Gepner–Heller's connec…

Let $k$ be the base field, let $\mathcal{DM}_c(k)$ denote the triangulated category of constructible Voevodsky motives over $k$, and let the $\ell$-adic realisation be the relevant…

Let $S$ be a noetherian excellent finite dimensional base scheme of characteristic $0$. The Ayoub conjecture. The heart of the perverse homotopy t-structure on $\mathrm{DM}(S)$ is…

Tilting-bundle equivalence conjecture. Under this derived equivalence, the restriction of the functor to the heart of the exotic t-structure gives an equivalence of abelian categor…

Enhancement uniqueness conjecture. Then $\mathrm{T}$ admits a unique $\infty$-categorical enhancement.

Enhancement uniqueness conjecture. The homotopy category $h\mathcal{C}$ admits a unique $\infty$-categorical enhancement.

Motivic $t$-structure conjecture. There is a motivic $t$-structure on $\textup{DM}_{\textup{gm}}(k;\mathbb{Q})$ whose heart has semisimple part $\textup{Num}(k;\mathbb{Q})$, every…

HRS-tilt characterization conjecture. The aisle $cD^{\leq 0}$ contains no nonzero Ext-projective if and only if it is a shift of the HRS-tilt associated with some torsion pair…

Derived-equivalence conjecture. Given an arbitrary weighted projective line $cX$, Assertion holds for $cD=\mathcal{D}^b(cX)$.

Heart-equivalence conjecture. This natural map should be an equivalence of nonconnective $K$-theory spectra. The assertion would identify the $K$-theory of a boundedly $t$-structur…

Let $E$ be a small stable $\infty$-category equipped with a bounded $t$-structure. Write $\mathrm{K}_{-n}(E)$ for its negative nonconnective $K$-groups. Bounded t-structure vanishi…

Let $\Gamma_\Fl:\bD_{\mathrm{ren}}(\fD(\Fl^{\operatorname{aff}}_G)_\crit\operatorname{mod})\to\bD_{\mathrm{ren}}(\hg_\crit\operatorname{mod}_\nilp)$ be the global-sections functor,…

Let $A$ be an associative algebra and consider … Equip it with the two t-structures described in the source: $\mathrm{new}_1$, obtained by tensoring the new t-structure on the affi…

Let $\bD_{\mathrm{ren}}(\fD(\Fl^{\operatorname{aff}}_G)_\crit\operatorname{mod})$ carry the old and new t-structures, and let $J_\cla$ be the convolution objects indexed by…