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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The Brauer-Manin obstruction on algebraic stacks
代数栈 Brauer-Manin阻塞 Hasse原理
2023/11/29
The Brauer-Manin obstruction is an old topic in local-global principle of varieties. I will talk about Brauer-Manin obstruction on algebraic stacks and extend some classical results such as the exact ...
Vanishing of algebraic Brauer-Manin obstructions
Hasse principle weak approximation Brauer-Manin obstruction
2011/1/18
Let X be a smooth geometrically integral algebraic variety over a number field k with finitely generated geometric Picard group. We prove that under certain conditions, certain algebraic Brauer-Manin ...
On the Brauer-Manin obstruction for cubic surfaces
the Brauer-Manin obstruction cubic surfaces
2010/11/11
We describe a method to compute the Brauer-Manin obstruction for smooth cubic surfaces over $\bbQ$ such that $\Br(S)/\Br(\bbQ)$ is of order two or four. This covers the vast majority of the cases when...
Brauer-Manin pairing, class field theory and motivic homology
Brauer group abelian fundamental group Wiesend’s ideal class group
2010/12/9
For a smooth proper variety over a p-adic field, the Brauer group and abelian fundamental group are related to the higher Chow groups by the Brauer-Manin pairing and the class field theory. We general...
For a smooth and projective variety over a number field with torsion free geometric Picard group and finite transcendental Brauer group we show that only the archimedean places, the primes of bad redu...