10 problems

Cyclic cohomology conjecture. The cyclic cohomology of $(H,R)$ satisfies

Let $(A,\Gamma)$ and $(B,\Sigma)$ be flat Hopf algebroids, and let a weak equivalence mean a morphism of flat Hopf algebroids inducing an equivalence between their comodule categor…

Let $\lambda$ be the decategorification functor from Definition, let $\mathsf{Meas}$ be the ambient category of measurable structures, and let $\mathsf{2Vect}^{BC}$ denote the 2-ca…

Let $(A,\mathcal U)$ be a co-commutative Hopf algebroid with an admissible filtration such that the translation map $\delta$ is filtered. Consider the diagram … In case…

Let $K/\mathbb{Q}_p$ be a finite field extension with ring of integers $A$, uniformizer $\pi$, and residue field $\mathbb{F}_q$. Ravenel's Local Conjecture. … where $I_n$ is the id…

Let $K/\mathbb{Q}$ be a finite Galois extension with ring of integers $A$. Let $J_n$ denote the minimal $n$-congruing ideal of $A$. Ravenel's Global Conjecture, stronger precise fo…

Let $K/\mathbb{Q}$ be a finite Galois extension with ring of integers $A$. An ideal $I$ of $A$ is $n$-congruing if, for every $a\in A$, there exists $N\in\mathbb{N}$ such that…

Let $K/\mathbb{Q}$ be a finite field extension with ring of integers $A$. For a prime ideal $\mathfrak{p}$ of $A$, write $A_{\mathfrak{p}}$ for the localization of $A$ at…

Hovey–Strickland's conjecture. The Hopf algebroids $(A,\mathcal H)$ and $(B,\mathcal K)$ are connected by a chain of weak equivalences.

Let ${\cal B}_{q,\lambda}(\widehat{sl}(M|N))$ be the elliptic quantum group associated with the affine Lie superalgebra $\widehat{sl}(M|N)$, and let $U_{q,p}(\widehat{sl}(M|N))$ be…