2025/03/12 by Julian Feuerpfeil, Feuerpfeil, Julian
Mathematics · #12G05 (Secondary) #16S37 (Primary) 12F10 #20J06 #FOS: Mathematics #Group Theory (math.GR) #K-Theory and Homology (math.KT) #Mathematical Approximation and Integration #Mathematical Dynamics and Fractals #Number Theory (math.NT) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2503.09264
openalex publication_date 2025/03/12 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28
Let p be a prime. An oriented pro-p group (G,θ) is said to have the Bogomolov--Positselski property if it is Kummerian and if Iθ(G) is a free pro-p group. In this paper, we provide a new criterion for an oriented pro-p group to satisfy the Bogomolov--Positselski property. This criterion builds on earlier work of Positselski (arXiv:1405.0965) and Quadrelli--Weigel (arXiv:2103.12438), relates their approaches, and answers a question raised in (arXiv:2103.12438). Under additional assumptions, we obtain two further sufficient criteria. The first is analogous to a Merkurjev--Suslin type statement. The second allows one to weaken the hypotheses appearing in Positselski's criterion (arXiv:1405.0965 Theorem 2). Finally, we show that the stronger conditions are satisfied by pro-p groups of elementary type. As a consequence, the Elementary Type Conjecture implies Positselski's ``Module Koszulity Conjecture 1'' (arXiv:1008.0095) for fields with finitely generated maximal pro-p Galois group.