| Abstrakt: |
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. [ABSTRACT FROM AUTHOR] |
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