Counterexamples to the local-global principle for non-singular plane curves and a cubic analogue of Ankeny-Artin-Chowla-Mordell conjecture

Yoshinosuke Hirakawa, Yosuke Shimizu

In this article, we introduce a systematic and uniform construction of non-singular plane curves of odd degrees $n\ge 5$ which violate the local-global principle. Our constructio…