The Brauer-Manin Obstruction and Cyclic Algebras
نویسندگان
چکیده
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.
منابع مشابه
The 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...
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