Failure of the Hasse Principle for Enriques Surfaces
نویسندگان
چکیده
We construct an Enriques surface over Q with empty étale-Brauer set (and hence no rational points) for which there is no algebraic Brauer-Manin obstruction to the Hasse principle. In addition, if there is a transcendental obstruction on our Enriques surface, then we obtain a K3 surface that has a transcendental obstruction to the Hasse principle.
منابع مشابه
Insufficiency of the Brauer-manin Obstruction for Enriques Surfaces
In [VAV11], Várilly-Alvarado and the last author constructed an Enriques surface X over Q with an étale-Brauer obstruction to the Hasse principle and no algebraic Brauer-Manin obstruction. In this paper, we show that the nontrivial Brauer class of XQ does not descend to Q. Together with the results of [VAV11], this proves that the BrauerManin obstruction is insufficient to explain all failures ...
متن کاملFailure of the Hasse principle for Châtelet surfaces in characteristic 2
Given any global field k of characteristic 2, we construct a Châtelet surface over k that fails to satisfy the Hasse principle. This failure is due to a Brauer-Manin obstruction. This construction extends a result of Poonen to characteristic 2, thereby showing that the étale-Brauer obstruction is insufficient to explain all failures of the Hasse principle over a global field of any characteristic.
متن کامل0 Fe b 20 09 THE HASSE PRINCIPLE FOR CHÂTELET SURFACES IN CHARACTERISTIC 2
Given any global field k of characteristic 2, we construct a Châtelet surface over k which fails to satisfy the Hasse principle. This failure is due to a Brauer-Manin obstruction. This construction extends a result of Poonen to characteristic 2, thereby showing that the étale-Brauer obstruction is insufficient to explain all failures of the Hasse principle over a global field of any characteris...
متن کاملOn the Arithmetic of Del Pezzo Surfaces of Degree 2
Del Pezzo surfaces are smooth projective surfaces, isomorphic over the algebraic closure of the base ,eld to P P or the blow-up of P in up to eight points in general position. In the latter case the del Pezzo surface has degree equal to 9 minus the number of points in the blow-up. The arithmetic of del Pezzo surfaces over number ,elds is an active area of investigation. It is known that the Has...
متن کاملMore cubic surfaces violating the Hasse principle
We generalize L. J. Mordell’s construction of cubic surfaces for which the Hasse principle fails.
متن کامل