Two examples of Brauer-Manin obstruction to integral points
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چکیده
منابع مشابه
Two Examples of Brauer–manin Obstruction to Integral Points
We give two examples of Brauer–Manin obstructions to integral points on open subsets of the projective plane.
متن کاملOn the Brauer–manin Obstruction for Integral Points
We give examples of Brauer–Manin obstructions to integral points on open subsets of the projective plane.
متن کاملThe Brauer–Manin obstruction
Let X be a smooth, geometrically irreducible variety over a field k. Recall that the defining property of an Azumaya algebra A is that, for any field K containing k and any point P ∈ X(K), we can evaluate A at P to get a central simple algebra A(P ) over K. In particular, suppose that k is a number field. Then, for each place v of k, we can evaluate A at points of X(kv) to get central simple al...
متن کاملEfficient evaluation of the Brauer – Manin obstruction
The Brauer–Manin obstruction is a concept which has been very effective in finding counter-examples to the Hasse principle, that is, sets of polynomial equations which have solutions in every completion of the rational numbers but have no rational solutions. The standard way of calculating the Brauer–Manin obstruction involves listing all the p-adic solutions to some accuracy, at finitely many ...
متن کاملThe Brauer-Manin Obstruction and Cyclic Algebras
Borrowing from a classical construction for counterexamples to the Hasse principle, we show that for a certain family of affine varieties which do not satisfy the Hasse principle, the Brauer-Manin obstruction is not satisfied. The approach is elementary and requires little algebraic geometry.
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2008
ISSN: 0024-6093
DOI: 10.1112/blms/bdn081