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

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8 papers · 1 filter

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.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.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…

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

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

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

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