Browse › Number theory › 018 The Margulis–Platonov conjecture over global fields
The Margulis–Platonov conjecture over global function fields
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Abstract
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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Possibly relevant literature (found by the agent, not checked)
- Andrei S. Rapinchuk, The congruence subgroup property for S-arithmetic subgroups of simple algebraic groups when S has positive Dirichlet density (arXiv:2603.27472, March 2026). Proves triviality of congruence kernels over number fields assuming the Margulis–Platonov conjecture; relevant to the introduction's remarks on the conjecture's role in the congruence subgroup problem, and cited by the number-field companion but not by this paper.
- Gopal Prasad and Andrei S. Rapinchuk, On the congruence kernel for simple algebraic groups (arXiv:1503.03713, March 2015). Studies congruence kernels over arbitrary global fields (including function fields) for infinite sets of places, context for the congruence-subgroup motivation stated in the introduction.
Digests and expositions
- Platzi ("Platzi Team"), Normal subgroups and the Margulis–Platonov conjecture (Platzi course "OpenAI Math Preprints", lesson 42; undated). Short video lesson with written summary of this preprint, covering the reduction to $\mathrm{SU}(D,*)$ and the replacement of the Furstenberg–Katznelson step by finite additive Fourier analysis; the page does not state how it was produced.
Elsewhere
- Emergent Mind: family 018
Independent sites; their content is not reviewed here.
Cite
@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}
}Family 018: The Margulis–Platonov conjecture over global fields
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.
Other papers in this family:
- The Margulis–Platonov conjecture over number fields · September 23, 2026