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arXiv · 1912.04620

Counterexamples to the local-global principle associated with Swinnerton-Dyer's cubic form

Yoshinosuke Hirakawa
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Abstract

In this paper, we imitate a classical construction of a counterexample to the local-global principle of cubic forms of 4 variables which was discovered first by Swinnerton-Dyer (Mathematica (1962)). Our construction gives new explicit families of counterexamples in homogeneous forms of $4, 5, 6, ..., 2n+2$ variables of degree $2n+1$ for infinitely many integers $n$. It is contrastive to Swinnerton-Dyer's original construction that we do not need any concrete calculation in the proof of local solubility.

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BibTeXRIS

Yoshinosuke Hirakawa. 2019-12-10. Counterexamples to the local-global principle associated with Swinnerton-Dyer's cubic form. https://arxiv.org/abs/1912.04620

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