7 problems

Let $p\geqslant 2$ be a prime number and let $(S,N)$ be a $\mathbb{Z}_p^m$-action of signature $(0;p^{n+1})$, where $2\leqslant m\leqslant n-1$. For each subgroup $L\leqslant N$ wi…

Let $X$ be a rationally connected variety of dimension $3$, and let $G\subset \mathrm{Bir}(X)$ be a finite abelian group. By the third type, we mean the case in which $G$ faithfull…

Spherical orbit-space conjecture. The space $N(P,\lambda)$ is homeomorphic to $S^n$ if and only if

Let $M$ be a compact differentiable manifold, and let $G$ be a finite subgroup of the diffeomorphism group of $M$. Ghys's conjecture. There is a constant $I$ such that $G$ has a ni…

Let $G$ be a finite group, and let $\operatorname{prim}(G)$ denote its primitivity invariant and $\operatorname{Sm}(G)$ its Smith invariant. Laitinen's conjecture. If … then … The…

Let $G$ be an Oliver group and let $N$ be a normal subgroup such that … is a monomorphism. A finite group is an Oliver group if it satisfies the Oliver condition, and a Smith exoti…

Let $M$ be a closed orientable $4$-manifold with Euler characteristic $(M) \neq 0$, and let $G$ be a finite group acting effectively, locally linearly, and homologically trivially…