13 problems

Barnea–Shalev's Hausdorff spectrum characterization conjecture
arXiv@arxiv
Let $G$ be a pro- $p$ group, and let $\operatorname{hspec}^{\mathcal G}(G)$ denote its Hausdorff spectrum with respect to a filtration $\mathcal G$ . A pro- $p$ group is $p$ -adic anal…
Conjectureopenhausdorff-dimension p-adic-analytic-groups profinite-groups
0
Prasad's comparison conjecture for second cohomology of p-adic analytic groups
arXiv@arxiv
Let $P$ be a pro- $p$ group, and write … Let $\varphi^2:H_{\operatorname{cont}}^{2}(P)\to H_{\operatorname{disc}}^{2}(P)$ be the comparison map. Prasad's conjecture. For every $p$ -a…
Conjectureopengroup-cohomology p-adic-analytic-groups pro-p-groups
1
Uniform weak Fontaine–Mazur conjecture
arXiv@arxiv
Let $K$ be a number field and let $L/K$ be an everywhere unramified Galois pro- $p$ extension. A pro- $p$ group is uniform if it is a uniform pro- $p$ group in the sense of Lazard. Un…
Conjectureopennumber-fields p-adic-analytic-groups pro-p-groups
1
Weak Fontaine–Mazur conjecture for unramified pro-p extensions
arXiv@arxiv
Let $K$ be a number field. An unramified pro- $p$ -extension is a Galois pro- $p$ extension of $K$ unramified at every place. Weak Fontaine–Mazur conjecture. Every unramified pro- $p$ -…
Conjectureopennumber-fields p-adic-analytic-groups pro-p-groups
1
The classification conjecture for strongly hereditarily self-similar pro-p groups
arXiv@arxiv
Classification conjecture. $G$ is strongly hereditarily self-similar of index $p$ if and only if $G$ is isomorphic to
Conjectureopenp-adic-analytic-groups pro-p-groups self-similar-groups
0
The self-similarity conjecture for three-dimensional Lie lattices of quaternionic type
arXiv@arxiv
Quaternionic self-similarity conjecture. Then $L$ is not self-similar.
Conjectureopenlie-lattices p-adic-analytic-groups self-similarity
0
The index invariance conjecture for isomorphic open subgroups
arXiv@arxiv
Index invariance conjecture. If $H\simeq K$ , then
Conjectureopenjust-infinite-groups p-adic-analytic-groups pro-p-groups
0
The self-similarity conjecture for open subgroups of norm-one quaternion groups
arXiv@arxiv
Self-similarity conjecture. For all primes $p\geqslant 5$ , no open subgroup of $SL_1^1(\Delta_p)$ is self-similar. For all primes $p\geqslant 3$ , no open subgroup of…
Conjectureopenp-adic-analytic-groups pro-p-groups self-similarity
1
The one-based/field-like dichotomy conjecture for full uniformly powerful pro-p groups
arXiv@arxiv
Let $\mathcal{G}=(G,I)$ be a uniformly powerful pro- $p$ group that is full as a profinite group. For each $n$ , let $P_n(G)$ denote the corresponding term in the lower $p$ -series, a…
Conjectureopenmodel-theory p-adic-analytic-groups profinite-groups
0
Klopsch–Snopce's characterization conjecture for uniform pro-\p groups
arXiv@arxiv
Let $p$ be an odd prime and let $G$ be a torsion-free pro- $p$ group. Write $d(G)$ for the minimal number of generators of $G$ , and let $\dim(G)$ denote its dimension as a $p$ -adic…
Conjectureopenp-adic-analytic-groups powerful-groups pro-p-groups
1
The rank-and-generator characterisation of uniform pro-p groups
arXiv@arxiv
Let $p\geq 3$ and let $G$ be a pro- $p$ group. Write $d(G)$ for the minimal number of topological generators of $G$ , and define the rank by … A pro- $p$ group is uniform if it is fin…
Conjectureopengroup-theory p-adic-analytic-groups pro-p-groups
1
The minimal-generator characterisation of uniform pro-p groups
arXiv@arxiv
Let $p\geq 3$ and let $G$ be a torsion-free pro- $p$ group of finite rank. Write $d(G)$ for the minimal number of topological generators of $G$ , and let $\dim(G)$ denote its dimensi…
Conjectureopengroup-theory p-adic-analytic-groups pro-p-groups
1
The nice-prime hypothesis conjecture for derivation hypotheses in Chevalley-type Iwasawa algebras
arXiv@arxiv
Let $\Phi$ be a root system and let $G$ be a uniform pro- $p$ group of Chevalley type, with Iwasawa algebra $\Omega_G$ and Frobenius pair $(\Omega_G,\Omega_{G^p})$ . The prime $p$ is…
Conjectureopeniwasawa-algebras lie-theory p-adic-analytic-groups
0