arXiv subjects

Felipe Rivera-Mesas

Publications and source records attributed to Felipe Rivera-Mesas.

4 recordsLinked to original sources

arXiv2026

Lichtenbaum-van Hamel duality for singular varieties over $p$-adic fields

In this article, we extend the van Hamel-Lichtenbaum duality theorem to (not necessarily smooth) proper and geometrically integral varieties defined over a $p$-adic field $k$. More precisely, we prove that for such variety $X$ there exists a natural continuous perfect pairing \[ \mathrm{Br}_1(X)\times H_0(X,\mathbb{Z})_τ^{\wedge} \to \mathbb{Q}/\mathbb{Z}, \] where $\mathrm{Br}_1(X):=\ker(\mathrm{Br}(X)\to\mathrm{Br}(\overline{X}))$ is the algebraic Brauer group of $X$, $H_0(X,\mathbb{Z})_τ$ is the zeroth group of truncated homology $\mathrm{Hom}_{D(k_{\mathrm{sm}})}(τ_{\leq 1}Rϕ_*\mathbb{G}_{m,X},\mathbb{G}_{m,k})$, $ϕ$ is the structure morphism of $X$, and $(-)^{\wedge}$ is the profinite completion functor.

math.NT↗

arXiv2025

Topologies on abelian groups and a topological five-lemma

In this article we establish some results that allow to deduce the continuity of homomorphisms of (topological) abelian groups from commutative diagrams. In particular, we present a new topological version of the classical Five-Lemma. These results aim to be applied in duality results between cohomology groups in arithmetical contexts. In such a topological-arithmetical context, Pontryagin duality plays a central role and it becomes necessary to know whether certain homomorphisms are continuous.

math.GN↗

arXiv2021

Hasse norm principle for Galois dihedral extensions

Let $L/k$ an Galois extension of number fields with Galois group isomorphic to a dihedral group of order $2n$. In this note, we give a general description of the Hasse norm principle for $L/k$ and the weak approximation for the norm one torus $R^1_{L/k}(\mathbb{G}_m)$ associated to $L/k$.

math.NT↗

arXiv2021

Bad places for the approximation property for finite groups

Given a number field $k$ and a finite $k$-group $G$, the Tame Approximation Problem for $G$ asks whether the restriction map $H^1(k,G)\to\prod_{v\inΣ}H^1(k_v,G)$ is surjective for every finite set of places $Σ\subseteqΩ_k$ disjoint from $\text{Bad}_G$, where $\text{Bad}_G$ is the finite set of places that either divides the order of $G$ or ramifies in the minimal extension splitting $G$. In this paper we prove that the set $\text{Bad}_G$ is "sharp". To achieve this we prove that there are finite abelian $k$-groups $A$ where the map $H^1(k,A)\to\prod_{v\inΣ_0}H^1(k_v,A)$ is not surjective in a set $Σ_0\subseteq\text{Bad}_A$ with particular properties, namely $Σ_0$ is the set of places that do not divide the order of $A$ and ramify in the minimal extension splitting $A$.

math.NT↗