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arXiv · 2604.14420

Failure of Weak Approximation in Adjoint Groups

Chayansudha Biswas
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Abstract

Platonov in 1991 conjectured that adjoint groups are rational as varieties over arbitrary infinite fields, and as a consequence have weak approximation. The rationality part of the conjecture was disproved by Merkurjev in 1996, but the question about weak approximation remained open. We settle this in the negative.

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Chayansudha Biswas. 2026-04-15. Failure of Weak Approximation in Adjoint Groups. https://arxiv.org/abs/2604.14420

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