Results 1 
7 of
7
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 ..."
Abstract

Cited by 7 (4 self)
 Add to MetaCart
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
VERTICAL BRAUER GROUPS AND DEL PEZZO SURFACES OF DEGREE 4
"... We show that Brauer classes of a locally solvable degree 4 del Pezzo surface X are vertical for some projection away from a plane g: X �� � P 1, i.e., that every Brauer class is obtained by pullback from an element of Br k(P 1). As a consequence, we prove that a Brauer class obstructs the existenc ..."
Abstract
 Add to MetaCart
We show that Brauer classes of a locally solvable degree 4 del Pezzo surface X are vertical for some projection away from a plane g: X �� � P 1, i.e., that every Brauer class is obtained by pullback from an element of Br k(P 1). As a consequence, we prove that a Brauer class obstructs the existence of a krational point if and only if all kfibers of g fail to be locally solvable, or in other words, if and only if X is covered by curves that each have no adelic points. The proof is constructive and gives a simple and practical algorithm, distinct from that in [BBFL07], for computing all classes in the Brauer group of X (modulo constant algebras).
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 ..."
Abstract
 Add to MetaCart
(Show Context)
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