11 problems

Balmer's Nerves of Steel Conjecture. The map $\phi$ is bijective. This conjecture seeks to reconcile the homological and triangular spectra of a rigid tensor-triangulated category.…

Balmer's comparison-map conjecture. For every finite group $G$, the comparison map is a homeomorphism

Property PB conjecture. All restricted Lie algebras satisfy Property PB regardless of representation type.

Property PC conjecture. For any restricted Lie algebra ${\mathfrak g}$ over $k$, ${\mathfrak g}$ satisfies Property PC if and only if ${\mathfrak g}$ is of tame or finite represent…

Let $0 \le i \le n+1$. For $i \le n$, let $\mathcal D_i$ be the full subcategory of dualizable objects $X$ in $\Sp_{k,n}^{\dual}$ that are retracts of $Y \wedge Z$ for some dualiza…

Let $\cat K$ be an essentially small tensor triangulated category. Write $\Spch(\cat K)$ for its homological spectrum, $\Spc(\cat K)$ for its Balmer spectrum, and … for the canonic…

Equivariant E(n)-local spectrum image conjecture. The map $\varphi_G$ is a homeomorphism onto its image.

Let $SH(\mathbb{F}_q)^c_\mathbb{Q}$ be the compact rational stable motivic homotopy category over $\mathbb{F}_q$, and let $\operatorname{Spc}$ denote its tensor-triangular spectrum…

The $\log_p$-conjecture. For all $n\geq r$, one has

Let $\mathscr{T}$ be a compactly generated $\otimes$-triangulated category and let $\mathscr{U}$ be a compactly generated triangulated category, both with all coproducts. Suppose ……

Spectrum conjecture. For every finite group $G$, the natural map