TRANSCHROMATIC EXTENSIONS IN MOTIVIC BORDISM

Agnès Beaudry; Michael A. Hill; Xiaolin Danny Shi; Mingcong Zeng

doi:10.1090/bproc/108

TRANSCHROMATIC EXTENSIONS IN MOTIVIC BORDISM

Agnès Beaudry, Michael A. Hill, Xiaolin Danny Shi, Mingcong Zeng

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1 Scopus citations

Abstract

We show a number of Toda brackets in the homotopy of the mo-tivic bordism spectrum MGL and of the Real bordism spectrum MU_R.These brackets are “red-shifting” in the sense that while the terms in the bracket will be of some chromatic height n, the bracket itself will be of chromatic height pn ` 1q. Using these, we deduce a family of exotic multiplications in the π_p˚,˚qMGL-module structure of the motivic Morava K-theories, including non-trivial multiplications by 2. These in turn imply the analogous family of exotic multiplications in the π_‹MU_R-module structure on the Real Morava K-theories.

Original language	English (US)
Pages (from-to)	76-90
Number of pages	15
Journal	Proceedings of the American Mathematical Society, Series B
Volume	10
DOIs	https://doi.org/10.1090/bproc/108
State	Published - 2023
Externally published	Yes

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abstract = "We show a number of Toda brackets in the homotopy of the mo-tivic bordism spectrum MGL and of the Real bordism spectrum MUR.These brackets are “red-shifting” in the sense that while the terms in the bracket will be of some chromatic height n, the bracket itself will be of chromatic height pn ` 1q. Using these, we deduce a family of exotic multiplications in the πp˚,˚qMGL-module structure of the motivic Morava K-theories, including non-trivial multiplications by 2. These in turn imply the analogous family of exotic multiplications in the π‹MUR-module structure on the Real Morava K-theories.",

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AU - Beaudry, Agnès

AU - Hill, Michael A.

AU - Shi, Xiaolin Danny

AU - Zeng, Mingcong

PY - 2023

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AB - We show a number of Toda brackets in the homotopy of the mo-tivic bordism spectrum MGL and of the Real bordism spectrum MUR.These brackets are “red-shifting” in the sense that while the terms in the bracket will be of some chromatic height n, the bracket itself will be of chromatic height pn ` 1q. Using these, we deduce a family of exotic multiplications in the πp˚,˚qMGL-module structure of the motivic Morava K-theories, including non-trivial multiplications by 2. These in turn imply the analogous family of exotic multiplications in the π‹MUR-module structure on the Real Morava K-theories.

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TRANSCHROMATIC EXTENSIONS IN MOTIVIC BORDISM

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