Diego Izquierdo

activity

20162025

most citedAutour d'une conjecture de Kato et Kuzumaki

8 citations · 12 across the 12 of their papers we have counts for

collaborators

12 papers

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.AG2025

Product of Brauer--Manin obstruction for 0-cycles over number fields and function fields

Diego Izquierdo, Yongqi Liang, Hui Zhang

It is conjectured that the Brauer--Manin obstruction is expected to control the existence of 0-cycles of degree 1 on smooth proper varieties over number fields. In this paper, we p…

math.GR2024

Tessellations of an affine apartment by affine weight polytopes

Claudio Bravo, Auguste Hébert, Diego Izquierdo +1

Let $\A$ be a finite dimensional vector space and $Φ$ be a finite root system in $\A$. To this data is associated an affine poly-simplicial complex. Motivated by a forthcoming cons…

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.AG2021★ 1 cited

Local-global principles for homogeneous spaces over some two-dimensional geometric global fields

Diego Izquierdo, Giancarlo Lucchini Arteche

In this article, we study the obstructions to the local-global principle for homogeneous spaces with connected or abelian stabilizers over finite extensions of the field $\mathbb{C…

math.GR2020

$Λ$ -buildings associated to quasi-split groups over $Λ$ -valued fields

Auguste Hébert, Diego Izquierdo, Benoit Loisel

Let $G$ be a quasi-split reductive group and $K$ be a Henselian field equipped with a valuation $ω : K^{\times} \to Λ$ , where $Λ$ is a non-zero tota…

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

Vanishing theorems and Brauer-Hasse-Noether exact sequences for the cohomology of higher-dimensional fields

Diego Izquierdo

Let $k$ be a finite field, a $p$ -adic field or a number field. Let $K$ be a finite extension of the Laurent series field in $m$ variables $k ((x_{1}, ..., x_{m}))$ or, more generally, a f…

math.AG2017★ 8 cited

Autour d'une conjecture de Kato et Kuzumaki

Diego Izquierdo

In 1986, Kato and Kuzumaki stated several conjectures in order to give a diophantine characterization of cohomological dimension of fields. In this article, we first prove a local-…

math.AG2016★ 1 cited

Dualité et principe local-global sur des corps locaux de dimension 2

Diego Izquierdo

Let $k$ be an algebraically closed field, a finite field or a $p$ -adic field. Let $K_{0} = k ((x, y))$ be the field of Laurent series in two variables over $k$ . We define Tate-Shafarevic…

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

Product of Brauer--Manin obstruction for 0-cycles over number fields and function fields

Tessellations of an affine apartment by affine weight polytopes

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

Local-global principles for homogeneous spaces over some two-dimensional geometric global fields

Λ-buildings associated to quasi-split groups over Λ-valued fields

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

Vanishing theorems and Brauer-Hasse-Noether exact sequences for the cohomology of higher-dimensional fields

Autour d'une conjecture de Kato et Kuzumaki

Dualité et principe local-global sur des corps locaux de dimension 2

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

$Λ$ -buildings associated to quasi-split groups over $Λ$ -valued fields

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