Year: 2025
Type: article
Abstract: Let $p$ be a prime number and let $F$ be a field of characteristic different from $p$ . We prove that there exist a field extension $L/F$ and $a,b,c,d$ in $L^{\times }$ such that $(a,b)=(b,c)=(c,d)=0$ in $\mathrm {Br}(L)[p]$ but the mod p Massey product $\langle a,b,c,d\rangle$ is not defined over $L$ . Thus, the strong Massey vanishing conjecture at the prime $p$ fails for $L$ , and the cochain differential graded ring $C^{* }(\Gamma _L,\mathbb Z/p\mathbb Z)$ of the absolute Galois group $\Gamma _L$ of $L$ is not formal. This answers a question of Positselski. As our main tool, we define a secondary obstruction that detects non-triviality of unramified torsors under tori, and which is of independent interest.
Source: Compositio Mathematica
Authors: Alexander Merkurjev, Federico Scavia
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,450
OpenAlex ID: W4413194444