17 citations · 30 across the 8 of their papers we have counts for
9 papers
On everywhere locally soluble varieties in families over toric bases
Vladi Mitankin, Leo Schäfer, Damaris Schindler +1
We determine the density of locally soluble fibres in certain families of varieties over a toric base. For this we develop a new form of the hyperbola method for toric bases which…
Local-global principles for semi-integral points on Markoff orbifold pairs
Vladimir Mitankin, Justin Uhlemann
We study local-global principles for semi-integral points on orbifold pairs of Markoff type. In particular, we analyse when these orbifold pairs satisfy weak weak approximation, we…
Cubic surfaces failing the integral Hasse principle
Julian Lyczak, Vladimir Mitankin, H. Uppal
We study the integral Brauer--Manin obstruction for affine diagonal cubic surfaces, which we employ to construct the first counterexamples to the integral Hasse principle in this s…
Semi-integral Brauer-Manin obstruction and quadric orbifold pairs
Vladimir Mitankin, Masahiro Nakahara, Sam Streeter
We study local-global principles for two notions of semi-integral points, termed Campana points and Darmon points. In particular, we develop a semi-integral version of the Brauer-M…
Genus one fibrations and vertical Brauer elements on del Pezzo surfaces of degree 4
Vladimir Mitankin, Cecília Salgado
We consider a family of smooth del Pezzo surfaces of degree four and study the geometry and arithmetic of a genus one fibration with two reducible fibres for which a Brauer element…
Rational points on del Pezzo surfaces of degree four
Vladimir Mitankin, Cecília Salgado
We study the distribution of the Brauer group and the frequency of the Brauer--Manin obstruction to the Hasse principle and weak approximation in a family of smooth del Pezzo surfa…
Integral Hasse principle and strong approximation for Markoff surfaces
Daniel Loughran, Vladimir Mitankin
We study the failure of the integral Hasse principle and strong approximation for Markoff surfaces, as studied by Ghosh and Sarnak, using the Brauer-Manin obstruction.
Integral points on generalised affine Châtelet surfaces
Vladimir Mitankin
We show, conditionally on Schinzel's hypothesis, that the only obstruction to the integral Hasse principle for generalised affine Châtelet surfaces is the Brauer--Manin one.
Failures of the Integral Hasse Principle for Affine Quadric Surfaces
Vladimir Mitankin
Quadric hypersurfaces are well-known to satisfy the Hasse principle. However, this is no longer true in the case of the Hasse principle for integral points, where counter-examples…