June 2023 DENOMINATORS OF SPECIAL VALUES OF ζ-FUNCTIONS COUNT KU-LOCAL HOMOTOPY GROUPS OF MOD p MOORE SPECTRA
Andrew Salch
Rocky Mountain J. Math. 53(3): 915-935 (June 2023). DOI: 10.1216/rmj.2023.53.915

Abstract

For each odd prime p, we show that the orders of the KU-local homotopy groups of the mod p Moore spectrum are equal to denominators of special values of certain quotients of Dedekind zeta-functions of totally real number fields. With this observation in hand, we give a cute topological proof of the Leopoldt conjecture for those number fields, by showing that it is a consequence of periodicity properties of KU-local stable homotopy groups.

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Andrew Salch. "DENOMINATORS OF SPECIAL VALUES OF ζ-FUNCTIONS COUNT KU-LOCAL HOMOTOPY GROUPS OF MOD p MOORE SPECTRA." Rocky Mountain J. Math. 53 (3) 915 - 935, June 2023. https://doi.org/10.1216/rmj.2023.53.915

Information

Received: 16 May 2020; Revised: 10 June 2022; Accepted: 9 July 2022; Published: June 2023
First available in Project Euclid: 21 July 2023

MathSciNet: MR4617921
zbMATH: 07731155
Digital Object Identifier: 10.1216/rmj.2023.53.915

Subjects:
Primary: 11M06 , 11R42 , 55Q10 , 55Q45 , 55Q51

Keywords: algebraic number theory , Algebraic Topology , Bousfield localization , Dedekind zeta-functions , Leopoldt conjecture , L-functions , p-adic regulators , special values , special values of L-functions , special values of zeta-functions , stable homotopy , stable homotopy groups

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.53 • No. 3 • June 2023
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