2022/03/17 by Han Wu, Wu, Han
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Advanced Topology and Set Theory
paper · pdf · doi:10.48550/arxiv.2203.09156
For Châtelet surfaces defined over number fields, we study two arithmetic properties, the Hasse principle and weak approximation, when passing to an extension of the base field. Generalizing a construction of Y. Liang, we show that for an arbitrary extension of number fields L/K, there is a Châtelet surface over K which does not satisfy weak approximation over any intermediate field of L/K, and a Châtelet surface over K which satisfies the Hasse principle over an intermediate field L' if and only if [L' : K] is even.