Excellent rings in transchromatic homotopy theory

The purpose of this note is to verify that several basic rings appearing in transchromatic homotopy theory are Noetherian excellent normal domains and thus amenable to standard techniques from commutative algebra. In particular, we show that the coefficients of iterated localizations of Morava $E$-theory at the Morava $K$-theories are normal domains and also that the coefficients in the transchromatic character map for a fixed group form a normal domain.

Keywords

Morava $E$-theory, Lubin–Tate theory, chromatic homotopy theory, excellent ring

2010 Mathematics Subject Classification

13F40, 55N20

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This article was revised on June 29, 2022 to correct the names used for internal cross-references.

Received 1 June 2017

Received revised 14 July 2017

Published 31 January 2018