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ЖУРНАЛЫ // Известия Российской академии наук. Серия математическая // Архив

Изв. РАН. Сер. матем., 2025, том 89, выпуск 2, страницы 60–104 (Mi im9597)

Rational and $p$-adic analogues of J. H. C. Whitehead's conjecture

A. M. Mikhovich

Moscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University, Moscow

Аннотация: We show that subpresentations of aspherical prounipotent presentations over fields of characteristic zero and subpresentations of aspherical pro-$p$-presentations are aspherical. The results are regarded as affirmative answers to rational and $p$-adic analogs of J. H. C. Whitehead conjecture. Methods of affine group schemes make it possible to unify the presentation for pro-$p$-groups and pro-unipotent groups in characteristic zero. This approach, in particular, allows us to put a strict mathematical reason under the philosophy proposed by J.-P. Serre; applications of our results to the classical Whitehead's problem are discussed as well.
Bibliography: 52 titles.

Ключевые слова: prounipotent presentations, Whitehead asphericity conjecture.

УДК: 515.142.53+515.142.21

MSC: 55P60, 20G10, 20F05

Поступило в редакцию: 22.04.2024
Исправленный вариант: 24.09.2024

Язык публикации: английский

DOI: 10.4213/im9597



© МИАН, 2025