The perfectoid commutant of Lubin-Tate power series

Laurent Berger

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arXiv · 2202.02020

The perfectoid commutant of Lubin-Tate power series

Laurent Berger

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Abstract

Let LT be a Lubin-Tate formal group attached to a finite extension of Qp. By a theorem of Lubin-Sarkis, an invertible characteristic p power series that commutes with the elements of Aut(LT) is itself in Aut(LT). We extend this result to perfectoid power series, by lifting such a power series to characteristic zero and using the theory of locally analytic vectors in certain rings of p-adic periods. This allows us to recover the field of norms of the Lubin-Tate extension from its completed perfection.

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Laurent Berger. 2022-02-04. The perfectoid commutant of Lubin-Tate power series. https://arxiv.org/abs/2202.02020

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