[图书][B] The Brauer-Grothendieck group
JL Colliot-Thélène, AN Skorobogatov - 2021 - Springer
Jean-Louis Colliot-Thélène Alexei N. Skorobogatov Page 1 The Brauer– Grothendieck Group
Jean-Louis Colliot-Thélène Alexei N. Skorobogatov Ergebnisse der Mathematik und ihrer …
Jean-Louis Colliot-Thélène Alexei N. Skorobogatov Ergebnisse der Mathematik und ihrer …
On the fibration method for zero-cycles and rational points
Y Harpaz, O Wittenberg - Annals of Mathematics, 2016 - JSTOR
Conjectures on the existence of zero-cycles on arbitrary smooth projective varieties over
number fields were proposed by Colliot-Thélène, Sansuc, Kato and Saito in the 1980's. We …
number fields were proposed by Colliot-Thélène, Sansuc, Kato and Saito in the 1980's. We …
Rational points and zero-cycles on rationally connected varieties over number fields
O Wittenberg - arXiv preprint arXiv:1604.08543, 2016 - arxiv.org
We report on progress in the qualitative study of rational points on rationally connected
varieties over number fields, also examining integral points, zero-cycles, and non-rationally …
varieties over number fields, also examining integral points, zero-cycles, and non-rationally …
Rational points on fibrations with few non-split fibres
Y Harpaz, D Wei, O Wittenberg - Journal für die reine und …, 2022 - degruyter.com
We revisit the abstract framework underlying the fibration method for producing rational
points on the total space of fibrations over the projective line. By fine-tuning its dependence …
points on the total space of fibrations over the projective line. By fine-tuning its dependence …
On the equation NK/k(Ξ)=P(t)
D Wei - Proceedings of the London Mathematical Society, 2014 - academic.oup.com
For varieties given by an equation, where is the norm form attached to a field extension and
in is a non-zero polynomial, three topics have been investigated: computation of the …
in is a non-zero polynomial, three topics have been investigated: computation of the …
[PDF][PDF] The Brauer–Grothendieck group
JL Colliot-Thélene, AN Skorobogatov - Preprint, 2019 - wwwf.imperial.ac.uk
A less known event of 1968 in Paris was the publication of “Dix exposés sur la cohomologie
des schémas” by J. Giraud, A. Grothendieck, SL Kleiman, M. Raynaud and J. Tate. Included …
des schémas” by J. Giraud, A. Grothendieck, SL Kleiman, M. Raynaud and J. Tate. Included …
[HTML][HTML] Rational points and prime values of polynomials in moderately many variables
K Destagnol, E Sofos - Bulletin des Sciences Mathématiques, 2019 - Elsevier
We derive the Hasse principle and weak approximation for fibrations of certain varieties in
the spirit of work by Colliot-Thélène–Sansuc and Harpaz–Skorobogatov–Wittenberg. Our …
the spirit of work by Colliot-Thélène–Sansuc and Harpaz–Skorobogatov–Wittenberg. Our …
Descent on toric fibrations
AN Skorobogatov - Arithmetic and geometry, 2015 - books.google.com
We describe descent on families of torsors for a constant torus. A recent result of Browning
and Matthiesen then implies that the Brauer–Manin obstruction controls the Hasse principle …
and Matthiesen then implies that the Brauer–Manin obstruction controls the Hasse principle …
On the equation N_ {K/k}(\Xi)= P (t)
D Wei - arXiv preprint arXiv:1202.4115, 2012 - arxiv.org
For varieties given by an equation N_ {K/k}(\Xi)= P (t), where N_ {K/k} is the norm form
attached to a field extension K/k and P (t) in k [t] is a polynomial, three topics have been …
attached to a field extension K/k and P (t) in k [t] is a polynomial, three topics have been …
[HTML][HTML] Towards the Brauer–Manin obstruction on varieties fibred over the projective line
Y Liang - Journal of Algebra, 2014 - Elsevier
Abstract Recently Dasheng Wei proved that the Brauer–Manin obstruction is the only
obstruction to the Hasse principle for 0-cycles of degree 1 on some fibrations over the …
obstruction to the Hasse principle for 0-cycles of degree 1 on some fibrations over the …