Add to ORKG17 pagesInternational audienceWe construct a smooth and projective surface over an arbitrary number field that is a counterexample to the Hasse principle but has the infinite etale Brauer-Manin set. We also construct a surface with a unique rational point and the infinite etale Brauer-Manin set. The key new ingredient is the arithmetic of singular projective curves
International audienceWe generalize Weil's theorem on the number of rational points of smooth curves...
International audienceWe generalize Weil's theorem on the number of rational points of smooth curves...
Abstract. We give large families of Shimura curves defined by congruence conditions, all of whose tw...
17 pagesInternational audienceWe construct a smooth and projective surface over an arbitrary number ...
In this thesis, we study the Hasse principle for curves and K3 surfaces. We give several sufficient ...
In [19], Manin introduced a way to explain the failure of the Hasse principle for algebraic varietie...
We discuss a range of ways, extending existing methods, to demonstrate violations of the Hasse princ...
We discuss a range of ways, extending existing methods, to demonstrate violations of the Hasse princ...
Let X be a smooth projective variety defined over a number field K. A fundamental problem in arithme...
Abstract. We conjecture that if C is a curve of genus> 1 over a number field k such that C(k) = ...
We study Brauer-Manin obstructions to the Hasse principle and to weak approximation on algebraic sur...
We construct infinitely many Chatelet surfaces, degree 4 del Pezzo surfaces, and Enriques surfaces t...
A classical result of Colliot-Thélène and Sansuc states that the only obstruction to the Hasse pri...
A classical result of Colliot-Thélène and Sansuc states that the only obstruction to the Hasse pri...
International audienceWe generalize Weil's theorem on the number of rational points of smooth curves...
International audienceWe generalize Weil's theorem on the number of rational points of smooth curves...
International audienceWe generalize Weil's theorem on the number of rational points of smooth curves...
Abstract. We give large families of Shimura curves defined by congruence conditions, all of whose tw...
17 pagesInternational audienceWe construct a smooth and projective surface over an arbitrary number ...
In this thesis, we study the Hasse principle for curves and K3 surfaces. We give several sufficient ...
In [19], Manin introduced a way to explain the failure of the Hasse principle for algebraic varietie...
We discuss a range of ways, extending existing methods, to demonstrate violations of the Hasse princ...
We discuss a range of ways, extending existing methods, to demonstrate violations of the Hasse princ...
Let X be a smooth projective variety defined over a number field K. A fundamental problem in arithme...
Abstract. We conjecture that if C is a curve of genus> 1 over a number field k such that C(k) = ...
We study Brauer-Manin obstructions to the Hasse principle and to weak approximation on algebraic sur...
We construct infinitely many Chatelet surfaces, degree 4 del Pezzo surfaces, and Enriques surfaces t...
A classical result of Colliot-Thélène and Sansuc states that the only obstruction to the Hasse pri...
A classical result of Colliot-Thélène and Sansuc states that the only obstruction to the Hasse pri...
International audienceWe generalize Weil's theorem on the number of rational points of smooth curves...
International audienceWe generalize Weil's theorem on the number of rational points of smooth curves...
International audienceWe generalize Weil's theorem on the number of rational points of smooth curves...
Abstract. We give large families of Shimura curves defined by congruence conditions, all of whose tw...