G. Arteche

activity

20132026

most citedThe Grunwald problem and approximation properties for homogeneous spaces

26 citations · 61 across the 18 of their papers we have counts for

collaborators

19 papers

math.AC2026

The structure of automorphism groups of zero-dimensional monomial algebras

Roberto Díaz, Giancarlo Lucchini Arteche, Gonzalo Manzano-Flores

Let $A$ be a zero-dimensional monomial algebra over an algebraically closed field of characteristic zero, that is, a finite-dimensional quotient of a polynomial ring by a monomial…

math.AG2026

Real approximation for homogeneous spaces with finite stabilizers

David Harari, Nguyên M\d{a}nh Linh, Giancarlo Lucchini Arteche

We prove some new cases of real appoximation for homogeneous spaces with finite stabilizers and describe the state of the art around this question, giving proofs that are well-know…

math.AG2025

Equivariant automorphism group and real forms of complexity-one varieties

Giancarlo Lucchini Arteche, Ronan Terpereau

Let $G$ be a connected reductive real algebraic group. We prove that every real $G$ -variety of complexity one admits only finitely many pairwise non-isomorphic $(R, G)$ -for…

math.RA2025

Central simple algebras, Milnor $K$ -theory and homogeneous spaces over complete discretely valued fields of dimension 2

Philippe Gille, Diego Izquierdo, Giancarlo Lucchini Arteche

Let $K$ be a complete discretely valued field with residue field $K ˉ$ of dimension $1$ (not necessarily perfect). This occurs if and only if $K$ has dimension $2$ . We prove the…

math.NT2023

Transfer principles for Galois cohomology and Serre's conjecture II

Diego Izquierdo, Giancarlo Lucchini Arteche

In this article, we prove several transfer principles for the cohomological dimension of fields. Given a fixed field $K$ with finite cohomological dimension $δ$ , the two main ones…

math.AG2022

On composition of torsors

Mathieu Florence, Diego Izquierdo, Giancarlo Lucchini Arteche

Let $K$ be a field, let $X$ be a connected smooth $K$ -scheme and let $G, H$ be two smooth connected $K$ -group schemes. Given $Y \to X$ a $G$ -torsor and $Z \to Y$ an $H$ -torsor, we s…

math.AG2022★ 2 cited

On Kato and Kuzumaki's properties for the Milnor $K_{2}$ of function fields of $p$ -adic curves

Diego Izquierdo, Giancarlo Lucchini Arteche

Let $K$ be the function field of a curve $C$ over a $p$ -adic field $k$ . We prove that, for each $n, d \geq 1$ and for each hypersurface $Z$ in $P_{K}^{n}$ of degree $d$ with…

math.GR2021★ 4 cited

Quotients of the Bruhat-Tits tree by arithmetic subgroups of special unitary groups

Luis Arenas-Carmona, Claudio Bravo, Benoit Loisel +1

Let $K$ be the function field of a curve $C$ over a field $F$ of either odd or zero characteristic. Following the work by Serre and Mason on $SL_{2}$ , we study the…

math.AG2021★ 2 cited

On homogeneous spaces with finite anti-solvable stabilizers

Giancarlo Lucchini Arteche

We say that a group is anti-solvable if all of its composition factors are non-abelian. We consider a particular family of anti-solvable finite groups containing the simple alterna…

math.AG2019★ 3 cited

A decomposition of the Jacobian of a Humbert-Edge curve

Robert Auffarth, Giancarlo Lucchini Arteche, Anita M. Rojas

A \textit{Humbert-Edge curve of type} $n$ is a non-degenerate smooth complete intersection of $n - 1$ diagonal quadrics. Such a curve has an interesting geometry since it has a natur…

math.AG2019

Smooth quotients of principally polarized abelian varieties

Robert Auffarth, Giancarlo Lucchini Arteche

We give an explicit characterization of all principally polarized abelian varieties $(A, Θ)$ such that there is a finite subgroup of automorphisms $G$ of $A$ that preserve the numer…

math.AG2018

Homogeneous spaces, algebraic $K$ -theory and cohomological dimension of fields

Diego Izquierdo, Giancarlo Lucchini Arteche

Let $q$ be a non-negative integer. We prove that a perfect field $K$ has cohomological dimension at most $q + 1$ if, and only if, for any finite extension $L$ of $K$ and for any homo…

math.AG2018★ 2 cited

Smooth quotients of abelian surfaces by finite groups that fix the origin

Robert Auffarth, Giancarlo Lucchini Arteche, Pablo Quezada

Let $A$ be an abelian surface and let $G$ be a finite group of automorphisms of $A$ fixing the origin. Assume that the analytic representation of $G$ is irreducible. We give a clas…

math.AG2018

The Hasse principle for homogeneous spaces with nilpotent stabilizer (Le principe de Hasse pour les espaces homogènes à stabilisateur fini)

Giancarlo Lucchini Arteche

We prove that the Brauer-Manin obstruction is the only obstruction to the Hasse principle for homogeneous spaces with nilpotent stabilizer. We thus generalize recent results by Har…

math.NT2015★ 26 cited

The Grunwald problem and approximation properties for homogeneous spaces

Cyril Demarche, Giancarlo Lucchini Arteche, Danny Neftin

Given a group $G$ and a number field $K$ , the Grunwald problem asks whether given field extensions of completions of $K$ at finitely many places can be approximated by a single fie…

math.NT2015★ 4 cited

Weak approximation for homogeneous spaces: reduction to the case with finite stabilizer

Giancarlo Lucchini Arteche

We reduce the question about whether the Brauer-Manin obstruction to weak approximation for homogeneous spaces is the only obstruction to the "simpler" question of the particular c…

math.GR2015★ 6 cited

Extensions of algebraic groups with finite quotient and nonabelian 2-cohomology

Giancarlo Lucchini Arteche

For a finite smooth algebraic group $F$ over a field $k$ and a smooth algebraic group $G ˉ$ over the separable closure of $k$ , we define the notion of $F$ -kernel in $G ˉ$ and…

math.AG2013★ 5 cited

Groupe de Brauer non ramifié algébrique des espaces homogènes (The unramified algebraic Brauer group of homogeneous spaces)

Giancarlo Lucchini Arteche

Using a reduction of the Galois cohomology of a linear algebraic group $G$ to that of a certain finite subquotient, we give different formulas allowing the calculation of the unram…

math.NT2013★ 7 cited

Approximation faible et principe de Hasse pour des espaces homogènes à stabilisateur fini résoluble (Weak Approximation and Hasse Principle for homogeneous spaces with finite solvable stabilizer)

Giancarlo Lucchini Arteche

Soit $K$ un corps global et $G$ un $K$ -groupe fini résoluble. Sous certaines hypothèses sur une extension déployant $G$ , on démontre que l'espace homogène $V := G^{'} / G$ avec $G^{'}$ un $K…

The structure of automorphism groups of zero-dimensional monomial algebras

Real approximation for homogeneous spaces with finite stabilizers

Equivariant automorphism group and real forms of complexity-one varieties

Central simple algebras, Milnor K-theory and homogeneous spaces over complete discretely valued fields of dimension 2

Transfer principles for Galois cohomology and Serre's conjecture II

On composition of torsors

On Kato and Kuzumaki's properties for the Milnor K2​ of function fields of p-adic curves

Quotients of the Bruhat-Tits tree by arithmetic subgroups of special unitary groups

On homogeneous spaces with finite anti-solvable stabilizers

A decomposition of the Jacobian of a Humbert-Edge curve

Smooth quotients of principally polarized abelian varieties

Homogeneous spaces, algebraic K-theory and cohomological dimension of fields

Smooth quotients of abelian surfaces by finite groups that fix the origin

The Hasse principle for homogeneous spaces with nilpotent stabilizer (Le principe de Hasse pour les espaces homogènes à stabilisateur fini)

The Grunwald problem and approximation properties for homogeneous spaces

Weak approximation for homogeneous spaces: reduction to the case with finite stabilizer

Extensions of algebraic groups with finite quotient and nonabelian 2-cohomology

Groupe de Brauer non ramifié algébrique des espaces homogènes (The unramified algebraic Brauer group of homogeneous spaces)

Approximation faible et principe de Hasse pour des espaces homogènes à stabilisateur fini résoluble (Weak Approximation and Hasse Principle for homogeneous spaces with finite solvable stabilizer)

Central simple algebras, Milnor $K$ -theory and homogeneous spaces over complete discretely valued fields of dimension 2

On Kato and Kuzumaki's properties for the Milnor $K_{2}$ of function fields of $p$ -adic curves

Homogeneous spaces, algebraic $K$ -theory and cohomological dimension of fields