Reconstructing global fields from dynamics in the abelianized Galois group

DOI10.1007/s00029-019-0469-8zbMath1431.11110arXiv1706.04517OpenAlexW2626328754WikidataQ128218201 ScholiaQ128218201MaRDI QIDQ670157

Xin Li, Gunther Cornelissen, Matilde Marcolli, Harry Smit

Publication date: 18 March 2019

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.04517

zbMATH Keywords

class field theory\(L\)-seriesanabelian geometryBost-Connes systemNeukirch-Uchida theorem

Mathematics Subject Classification ID

Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Coverings of curves, fundamental group (14H30) Class field theory (11R37) Zeta functions and (L)-functions of number fields (11R42) Adèle rings and groups (11R56) Noncommutative geometry (à la Connes) (58B34) Relations with noncommutative geometry (11M55) Applications of functional analysis in statistical physics (46N55)

Related Items (4)

Quantum statistical mechanics of the absolute Galois group ⋮ Two-step nilpotent extensions are not anabelian ⋮ Constructing number field isomorphisms from \(*\)-isomorphisms of certain crossed product \(\mathrm{C}^*\)-algebras ⋮ Characterization of global fields by Dirichlet \(L\)-series

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