676 research outputs found
Norms as products of linear polynomials
Let F be a number field, and let F\subset K be a field extension of degree n.
Suppose that we are given 2r sufficiently general linear polynomials in r
variables over F. Let X be the variety over F such that the F-points of X
bijectively correspond to the representations of the product of these
polynomials by a norm from K to F. Combining the circle method with descent we
prove that the Brauer-Manin obstruction is the only obstruction to the Hasse
principle and weak approximation on any smooth and projective model of X.Comment: 25 page
Cohomology and the Brauer groups of diagonal surfaces
We present a method for calculating the Brauer group of a surface given by a
diagonal equation in the projective space. For diagonal quartic surfaces with
coefficients in Q we determine the Brauer groups over Q and Q(i).Comment: 45 page
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