9 problems

The Gersten conjecture. These complexes are exact whenever $R$ is a regular local ring. Here $K$ is the fraction field of $R$, and $k(q)$ is the residue field at $q$. The conjectur…

Let $Y$ be a canonical component of the character variety of a hyperbolic knot group, let $W\subseteq Y$ be the dense open subvariety parametrizing irreducible representations, and…

Let $X$ be a quasi-compact and quasi-separated scheme in which $p$ is invertible, and let $A$ and $A'$ be $p$-power torsion Azumaya algebras over $X$. The Künneth map is … Here…

Let $\widehat{X}$ be a small resolution of $X_{\vec{d}}$, let $S_{\vec{d},1}$ be the relevant singular locus, and let $f:\widehat{X}\to\mathbb{P}^3$ be the morphism in the construc…

Let $M$ be a hyperbolic once-punctured torus bundle, let $\widetilde{C}$ denote the relevant character-curve component, and let $\mathcal{A}_{k(\widetilde{C})}$ be its tautological…

Azumaya-positive knot conjecture. $K$ is not an $L$-space knot.

Let $n\geq 2$. An Azumaya algebra $A$ is an Azumaya algebra of degree $2^n$ and period $2$ over a commutative domain. Write $[A]$ for its Brauer class, and let $A'\in[A]$ be a repr…

Let $K$ be a subtorus of a torus $T$, let $\boldsymbol{\chi}=(\chi_i)$ be the associated characters, and let $\alpha$ be as in the construction of the hypertoric variety. For each…

Equality conjecture for the two Adams operations. The operations should agree: