13 problems

Let $\mathcal{A}$ be a smooth $\mathbb{C}$-linear stable $\infty$-category. The finite Quillen-Lichtenbaum dimension conjecture. Then … Here $\dim_{\mathrm{QL}}\mathcal{A}$ is the…

Let $X$ be a smooth separated scheme over $\mathbb{C}$ of finite type and let $A$ be an abelian group. The semi-topological Quillen-Lichtenbaum conjecture. The canonical map … is a…

Let $K$ be a compact connected Lie group, $T$ its maximal torus, and $\pi\colon K\rightarrow K/T$ the natural projection. Denote by $G=K_{\mathbb C}$ the corresponding split reduct…

Rosenberg's conjecture. 1. For $n>0$, the map

Let $\mathcal{C}$ be a $\mathbb{C}$-linear dg-category. Write $K_*^{\operatorname{top}}(\mathcal{C})$ for its topological $K$-theory groups and $HP_*(\mathcal{C})$ for its periodic…

Higher units conjecture. For all $n\geq 0$ there are equivalences

Brauer spectrum conjecture. There is an equivalence

The truncated Anderson dual conjecture. There is an equivalence of spectra

Let $\mathcal{T}$ be a smooth proper dg-category over $\mathbb{C}$. Write $K_{\operatorname{top}}(\mathcal{T})$ for its topological K-theory spectrum,…

K-theoretic computation conjecture.

Let $A$ be a real or complex commutative Banach algebra with involution, let $\varepsilon$ denote the hermitian sign, and let $m$ be the coefficient modulus. The algebraic-to-topol…

Let $\mathcal R$ be a root datum with affine Weyl group $W^e$, let $\Gamma$ be the finite group acting in the extended affine Hecke algebra, and let $q$ be a positive parameter fun…

Let $\Gamma<\operatorname{Isom}(\mathbb{R}^k)$ be a torsion-free crystallographic group. Its quotient $\mathbb{R}^k/\Gamma$ is a closed aspherical manifold, and…