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pro vyhledávání: '"Mitankin, Vladimir"'
Autor:
Mitankin, Vladimir, Uhlemann, Justin
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, weak approximation and strong approximation off a finite set of places.
Externí odkaz:
http://arxiv.org/abs/2411.02629
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 setting. We then count in three natural ways how such counterexamples a
Externí odkaz:
http://arxiv.org/abs/2311.10008
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-Manin obstruction interpolating between Manin's classical version for r
Externí odkaz:
http://arxiv.org/abs/2209.15582
Autor:
Mitankin, Vladimir, Salgado, Cecília
Publikováno v:
Published, J. Number Theory 236 (2022), 463-478
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 is vertical.
Comment: 17 pages. arXiv admin note: substantial te
Comment: 17 pages. arXiv admin note: substantial te
Externí odkaz:
http://arxiv.org/abs/2102.08798
Autor:
Mitankin, Vladimir, Salgado, Cecília
Publikováno v:
Published, Int. J. Number Theory 18 (2022), no. 9, 2099-2127
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 surfaces of degree four over the rationals.
Comment: 26 pages
Comment: 26 pages
Externí odkaz:
http://arxiv.org/abs/2002.11539
Autor:
Loughran, Daniel, Mitankin, Vladimir
Publikováno v:
Published, IMRN 18 (2021), 14086-14122
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.
Comment: 28 pages
Comment: 28 pages
Externí odkaz:
http://arxiv.org/abs/1807.10223
Autor:
Mitankin, Vladimir
Publikováno v:
Published, Bull. Sci. Math. 159 (2020), 102830, 20 pp
We show, conditionally on Schinzel's hypothesis, that the only obstruction to the integral Hasse principle for generalised affine Ch\^{a}telet surfaces is the Brauer--Manin one.
Comment: 17 pages, submitted
Comment: 17 pages, submitted
Externí odkaz:
http://arxiv.org/abs/1802.10012
Autor:
Mitankin, Vladimir, Salgado, Cecília
Publikováno v:
In Journal of Number Theory July 2022 236:463-478
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