7 problems

Hesselholt's descent conjecture. For all positive integers $q$, this canonical map is an isomorphism of pro-abelian groups, and the higher continuous cohomology groups of the pro-…

Let $K$ be a field with valuation ring $V$, residue field $k$, and let $\bar{K}$ be an algebraic closure of $K$ with Galois group $G_K$. Let $\bar{V}$ be the integral closure of…

Let $\bbS^{\widehat{\calN}}$ be the stack of one-dimensional commutative formal groups with a section, and let…

Let $X$ be a nice scheme over $\mathbf{F}_{p}$, let $K(X)$ denote its algebraic $K$-theory spectrum, and let $TC(X,p)$ denote its $p$-typical topological cyclic homology. Cyclotomi…

Let $R$ be a connective $E_{\infty}$ ring spectrum, and let … be the cyclotomic trace, where both spectra are $p$-completed. The cyclotomic-trace compatibility conjecture. The cycl…

Let $\operatorname{TR}^3_{13-\lambda_4}(\mathbb{Z};2)$ be the indicated equivariant topological Hochschild homology group, where $\lambda_4$ is the relevant $RO(S^1)$-representatio…

Let $\operatorname{TR}^3_{9-\lambda_4}(\mathbb{Z};2)$ be the indicated equivariant topological Hochschild homology group, where $\lambda_4$ is the relevant $RO(S^1)$-representation…