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NORM FORMS FOR ARBITRARY NUMBER FIELDS AS PRODUCTS OF LINEAR POLYNOMIALS
"... Abstract. Given a number field K/Q and a polynomial P ∈ Q[t], all of whose roots are in Q, let X be the variety defined by the equation NK(x) = P (t). Combining additive combinatorics with descent we show that the Brauer–Manin obstruction is the only obstruction to the Hasse principle and weak appr ..."
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Abstract. Given a number field K/Q and a polynomial P ∈ Q[t], all of whose roots are in Q, let X be the variety defined by the equation NK(x) = P (t). Combining additive combinatorics with descent we show that the Brauer–Manin obstruction is the only obstruction to the Hasse principle and weak approximation on any smooth and projective model of X. Contents
On the fibration method for zerocycles and rational points
 Annals of Math
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The number of varieties in a family which contain a rational point
, 2014
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A SURVEY OF APPLICATIONS OF THE CIRCLE METHOD TO RATIONAL POINTS
"... Given a number field k and a projective algebraic variety X defined over k, the question of whether X contains a krational point is both very natural and very difficult. In the event that the set X(k) of krational points is not empty, one can also ask how the points of X(k) are distributed. Are th ..."
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Given a number field k and a projective algebraic variety X defined over k, the question of whether X contains a krational point is both very natural and very difficult. In the event that the set X(k) of krational points is not empty, one can also ask how the points of X(k) are distributed. Are they dense in X
3 NORM FORMS FOR ARBITRARY NUMBER FIELDS AS PRODUCTS OF LINEAR POLYNOMIALS
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