Mináč–Tăn's vanishing conjecture for higher Massey products

Let FF be a field, let pp be a prime, let n3n\geq 3, and let χ1,,χnH1(F,Z/pZ)\chi_1,\dots,\chi_n\in H^1(F,\mathbb Z/p\mathbb Z). The Massey product χ1,,χnH2(F,Z/pZ)\left\langle\chi_1,\dots,\chi_n\right\rangle\subset H^2(F,\mathbb Z/p\mathbb Z) is defined when it is non-empty, and it vanishes when it contains 00.

Mináč–Tăn's conjecture. For every field FF, every prime pp, every n3n\geq 3, and all χ1,,χnH1(F,Z/pZ)\chi_1,\dots,\chi_n\in H^1(F,\mathbb Z/p\mathbb Z), if the Massey product

χ1,,χnH2(F,Z/pZ)\left\langle\chi_1,\dots,\chi_n\right\rangle\subset H^2(F,\mathbb Z/p\mathbb Z)

is defined, then it vanishes.

This conjecture proposes that every defined higher mod-pp Massey product in the cohomology of an absolute Galois group contains zero. The triple-product case is known for arbitrary fields, while the general case remains open in the stated formulation.

Sources & referencesView supporting material

Primary source

Alexander Merkurjev and Federico Scavia, “Degenerate fourfold Massey products over arbitrary fields”, arXiv:2208.13011 (2023).

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