[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 …
Zéro-cycles sur les espaces homogènes et problème de Galois inverse
Y Harpaz, O Wittenberg - Journal of the American Mathematical Society, 2020 - ams.org
Soit $ X $ une compactification lisse d'un espace homogène d'un groupe algébrique linéaire
$ G $ sur un corps de nombres $ k $. Nous établissons la conjecture de Colliot-Thélène …
$ G $ sur un corps de nombres $ k $. Nous établissons la conjecture de Colliot-Thélène …
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 …
Norm forms for arbitrary number fields as products of linear polynomials
TD Browning, L Matthiesen - … Scientifiques de l' …, 2017 - research-information.bris.ac.uk
Given a number field K/Q and a polynomial P ε Q [t], all of whose roots are Q, let X be the
variety defined by the equation NK (x)= P (t). Combining additive combinatiorics with …
variety defined by the equation NK (x)= P (t). Combining additive combinatiorics with …
Quadratic polynomials represented by norm forms
TD Browning, DR Heath-Brown - Geometric and Functional Analysis, 2012 - Springer
Abstract Let P (t) ∈ Q t be an irreducible quadratic polynomial and suppose that K is a
quartic extension of Q containing the roots of P (t). Let\bf N _ K/Q (\rm x) be a full norm form …
quartic extension of Q containing the roots of P (t). Let\bf N _ K/Q (\rm x) be a full norm form …
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 …
Supersolvable descent for rational points
Y Harpaz, O Wittenberg - Algebra & Number Theory, 2024 - msp.org
We construct an analogue of the classical descent theory of Colliot-Thélène and Sansuc in
which algebraic tori are replaced with finite supersolvable groups. As an application, we …
which algebraic tori are replaced with finite supersolvable groups. As an application, we …