V. D. Vries

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math.AG2026

K3 surfaces over $Q$ of degree $10$ that have Picard rank $1$

Victor de Vries

We give examples of K3 surfaces over $Q$ of degree $10$ whose geometric Picard group has rank~ $1$ . These K3 surfaces are intersections in $P^{9}$ of three hyperplan…

math.AG2025

Evaluating the tame Brauer group of open varieties over local fields

Victor de Vries

In this document we let $U$ be a smooth variety of pure dimension $d$ over a local field $k_{v}$ with unit ball $O_{v}$ and residue field $F$ of characteristic $p > 0$ …

math.AG2025

Description of the strong approximation locus using Brauer-Manin obstruction for homogeneous spaces with commutative stabilizers

Victor de Vries, Haowen Zhang

For a homogeneous space $X$ over a number field $k$ , the Brauer-Manin obstruction has been used to study strong approximation for $X$ away from a finite set $S$ of places, and know…

math.AG2024

Functorial splitting of $l$ -adic cohomology in exact sequences of group varieties

Victor de Vries

In this document we consider an exact sequence of group varieties $e \to N \to G \to Q \to e$ over an algebraically closed field. We show that for $l \neq = char (k)$ a prime ther…

K3 surfaces over Q of degree 10 that have Picard rank 1

Evaluating the tame Brauer group of open varieties over local fields

Description of the strong approximation locus using Brauer-Manin obstruction for homogeneous spaces with commutative stabilizers

Functorial splitting of l-adic cohomology in exact sequences of group varieties

K3 surfaces over $Q$ of degree $10$ that have Picard rank $1$

Functorial splitting of $l$ -adic cohomology in exact sequences of group varieties