Milnor invariants and Massey products for prime numbers

Masanori Morishita

doi:10.1112/S0010437X03000137

Abstract

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Following the analogy between primes and knots, we introduce the refined Milnor invariants for prime numbers and establish their connection with certain Massey products in Galois cohomology. This generalizes the well-known relation between the power residue symbol and cup product and gives a cohomological interpretation of L. Rédei's triple symbol.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Morishita, Masanori 2008. Geometry and Dynamics of Groups and Spaces. Vol. 265, Issue. , p. 669.

Jebali, Hajer 2009. Module d’Alexander et représentations métabéliennes. Annales de la Faculté des sciences de Toulouse : Mathématiques, Vol. 17, Issue. 4, p. 751.

Morishita, Masanori 2012. Knots and Primes. p. 85.

Amano, Fumiya 2014. On a certain nilpotent extension over $\boldsymbol{Q}$ of degree 64 and the 4-th multiple residue symbol. Tohoku Mathematical Journal, Vol. 66, Issue. 4,

Efrat, Ido 2014. The Zassenhaus filtration, Massey products, and representations of profinite groups. Advances in Mathematics, Vol. 263, Issue. , p. 389.

Efrat, Ido 2014. Single-Valued Massey Products. Communications in Algebra, Vol. 42, Issue. 11, p. 4609.

Gärtner, Jochen 2014. Rédei symbols and arithmetical mild pro-2-groups. Annales mathématiques du Québec, Vol. 38, Issue. 1, p. 13.

Gärtner, Jochen 2015. Higher Massey products in the cohomology of mild pro-p-groups. Journal of Algebra, Vol. 422, Issue. , p. 788.

Mináč, Ján and Tân, Nguyễn Duy 2015. The kernel unipotent conjecture and the vanishing of Massey products for odd rigid fields. Advances in Mathematics, Vol. 273, Issue. , p. 242.

Chapman, Michael and Efrat, Ido 2016. Filtrations of free groups arising from the lower central series. Journal of Group Theory, Vol. 19, Issue. 3, p. 405.

Morishita, Masanori and Terashima, Yuji 2017. p-Johnson homomorphisms and pro-p groups. Journal of Algebra, Vol. 479, Issue. , p. 102.

Amano, Fumiya Mizusawa, Yasushi and Morishita, Masanori 2018. On mod 3 triple Milnor invariants and triple cubic residue symbols in the Eisenstein number field. Research in Number Theory, Vol. 4, Issue. 1,

Guillot, Pierre Mináč, Ján and Topaz, Adam 2018. Four-fold Massey products in Galois cohomology. Compositio Mathematica, Vol. 154, Issue. 9, p. 1921.

Hirano, Hikaru and Morishita, Masanori 2019. Arithmetic topology in Ihara theory II: Milnor invariants, dilogarithmic Heisenberg coverings and triple power residue symbols. Journal of Number Theory, Vol. 198, Issue. , p. 211.

Efrat, Ido and Quadrelli, Claudio 2019. The Kummerian property and maximal pro-p Galois groups. Journal of Algebra, Vol. 525, Issue. , p. 284.

Mizusawa, Yasushi 2019. On pro-𝑝 link groups of number fields. Transactions of the American Mathematical Society, Vol. 372, Issue. 10, p. 7225.

El Habibi, Abdelaziz and Mizusawa, Yasushi 2022. On pro-p-extensions of number fields with restricted ramification over intermediate Zp-extensions. Journal of Number Theory, Vol. 231, Issue. , p. 214.

Lam, Yeuk Hay Joshua Liu, Yuan Sharifi, Romyar Wake, Preston and Wang, Jiuya 2023. Generalized Bockstein maps and Massey products. Forum of Mathematics, Sigma, Vol. 11, Issue. ,

Kodani, Hisatoshi and Terashima, Yuji 2023. Arithmetic Orr Invariants of Absolute Galois Groups. International Mathematics Research Notices, Vol. 2023, Issue. 13, p. 11316.

Lee, Jungin and Park, Jeehoon 2023. Arithmetic Chern–Simons theory with real places. Journal of Knot Theory and Its Ramifications, Vol. 32, Issue. 04,

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Milnor invariants and Massey products for prime numbers

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

Milnor invariants and Massey products for prime numbers

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