The Margulis–Platonov conjecture over global fields

2 papers

Proves the Margulis–Platonov conjecture over every global field, including function fields of characteristic two. For an absolutely almost simple simply connected algebraic group G over k, every noncentral abstract normal subgroup of \(G(k)\) is the inverse image of an open normal subgroup in the finite product of its anisotropic nonarchimedean local groups.

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▶Introduction: the problem and why it mattersin preparation

▶The presented solutionin preparation

Papers 2

The Margulis–Platonov conjecture over global function fields

OpenAI · October 5, 2026

We prove the Margulis–Platonov conjecture over every global function field, including characteristic two. For an absolutely almost simple simply connected algebraic group, every noncentral abstract normal subgroup of its rational points is the inverse image of an open normal subgroup of the finite product of its anisotropic local groups.

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@misc{OAI:The-Margulis-Platonov-conjecture-over-global-function-fields-October-5-2026,
  author = {{OpenAI}},
  title = {{The Margulis--Platonov conjecture over global function fields}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/The-Margulis-Platonov-conjecture-over-global-function-fields-October-5-2026/margulis-platonov-global-function-fields.pdf}{OAI:The-Margulis-Platonov-conjecture-over-global-function-fields-October-5-2026}},
  year = {2026}
}

The Margulis–Platonov conjecture over number fields

OpenAI · September 23, 2026

We prove the Margulis–Platonov conjecture over number fields. For an absolutely almost simple simply connected group, every noncentral abstract normal subgroup of its rational points is the inverse image of an open normal subgroup of the product of its anisotropic nonarchimedean local groups.

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Cite

@misc{OAI:The-Margulis-Platonov-conjecture-over-number-fields-September-23-2026,
  author = {{OpenAI}},
  title = {{The Margulis--Platonov conjecture over number fields}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/The-Margulis-Platonov-conjecture-over-number-fields-September-23-2026/paper.pdf}{OAI:The-Margulis-Platonov-conjecture-over-number-fields-September-23-2026}},
  year = {2026}
}

Formal verification

No Lean formalization is listed for this result yet. The repository notes that unformalized results could have issues.