Denominators of special values of zeta-functions count KU-local homotopy groups of mod p Moore spectra

A. Salch

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arXiv · 2303.09550

Denominators of special values of zeta-functions count KU-local homotopy groups of mod p Moore spectra

A. Salch

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Abstract

In this note, 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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A. Salch. 2023-03-16. Denominators of special values of zeta-functions count KU-local homotopy groups of mod p Moore spectra. https://arxiv.org/abs/2303.09550

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