9 problems

Namba's conjecture. The isomorphism type of $C$ is determined entirely by the branching of the projection $(x,y)\in C\mapsto x$.

Let $k\subset S^3$ be a knot with Alexander polynomial $\Delta$, and let $M_r$ be the $r$-fold cyclic cover of $S^3$ branched over $k$. The finite values of $|H_1(M_r)|$ are those…

Branching-data conjecture. The $a$-number of $\phi_n$ is uniquely determined by its branching datum.

Let $\Phi_\mathcal T$ be the perturbative power series of an ideal triangulation $\mathcal T$, and let the cyclic-cover loop invariants be those defined in the paper. The all-natur…

Let $k$ be the residue field of a discrete valuation ring $R$ of characteristic zero, and let $k[[z_2]]/k[[x]]$ be a cyclic $\Gamma$-extension with Galois sub-extension…

Let $k$ be an algebraically closed field of characteristic $p>0$. Let $\phi: Z \xrightarrow{} X$ be a cyclic $\Gamma$-cover of curves over $k$, and let $\phi_1: Y \xrightarrow{} X$…

Deformability in towers conjecture. If $G$ is cyclic, then the natural morphism

Let $m,n\geq 2$ and let $\boldsymbol{c}=(c_1,\ldots,c_{n-1})\in(\mathbb{Z}_{>0})^{n-1}$. For the families $\mathcal{F}_{d,n}^{\boldsymbol{c}}(\mathbb{F}_q)$ and…

Strong liftability conjecture. The scheme $Y$ is a smooth projective scheme which is strongly liftable over $W_2(k)$.