Descent obstruction and fundamental exact sequence
David Harari, Jakob Stix
备注：
20 pages - in this second version the applications (section 3) are reorganised as "abelian" applications (section 3) and "non-abelian" applications (section 4)
A torsor under a k-group scheme G on a variety X over a number field k imposes a descent obstruction against the existence of rational points on X. We discuss the finite descent obstruction, that is for all such torsors under finite k-groups G, in view of a local-global interpolation property for sections of the fundamental group short exact sequence of X/k. There are applications to the Brauer-Manin obstruction, to the descent obstruction by torsors under linear groups, and to the birational version of Grothendieck's section conjecture over number fields. In particular, we obtain examples of families of curves over number fields, such that the birational section conjecture is true in a non-trivial way.
Varietes de descente, gerbes et obstruction de Brauer-Manin (Descent varieties, gerbes and Brauer-Manin obstruction)
我们对布劳尔-马宁的一系列障碍物进行了界定，就像在各种情况下，全球部分的存在缺陷一样。Ceci nous conduit à une généralisation de la dualité de Tate-Poitou au cas non-abélien.我们找到了一种方法来关联到一个gerbe定义在数域上的Brauer-Manin阻塞，它的措施，作为品种，缺陷的存在一个整体瓣。这导致我们在非阿贝尔的情况下推广的Tate-Poitou对偶。
Comparing local-global obstructions on algebraic stacks
State Key Laboratory of Cyberspace Security Defense Institute of Information Engineering Chinese Academy of Sciences（中国科学院信息工程研究所网络空间安全防御国家重点实验室）；Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University（湖北大学数学与统计学院应用数学湖北省重点实验室）；School of Mathematical Sciences, Beihang University（北京航空航天大学数学科学学院）
Corrigendum à "Sous-groupe de Brauer invariant et obstruction de descente itérée" Algebra & Number Theory 14 (2020), no. 8, 2151--2183
我们的工作“Sous-groupe de Brauer invariant et obstruction de descente itérée”§2使用了Skorobogatov和Zarhin在他们的论文“The Brauer group and the Brauer-Manin set of products of varieties”中证明的关于二次Künneth公式的陈述。最近他们发现这种说法是不正确的（见他们的更正）。我们修正了论文的第2段。我们论文的其余部分仍然是正确的。
On commutative diagrams consisting of low term exact sequences
我们建立了几个有用的交换图表，这些图表由附在{ \Grot }谱序列上的低项正合序列组成。Skorobogatov [超越{M}anin障碍，发明。Math.（1999）]和[On the elementary obstruction to the existence of有理点，Mathematical Notes（2007）]。部分图中常采用局部-整体原则来求有理点。
