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Localizations of E-Theory and Transchromatic Phenomena in Stable Homotopy Theory

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homotopy theory studies a parametrization of stable homotopy theory in terms of algebraic objects called formal groups. Transchromatic homotopy theory is specifically concerned with the behavior of spaces and cohomology theories as these formal groups change in height. We pursue a central transchromatic object, the K(n āˆ’ 1)- localization of a height n Morava E-theory En. We give a modular description of the coefficients of LK(nāˆ’1)En in terms of deformations of formal groups together with extra data about the (n āˆ’ 1)th Lubin-Tate coordinate. We use this to describe co-operations and power operations in this transchromatic setting. As an application, we construct exotic multiplicative structures on LK(1)E2, not induced from the ring structure on E2 by K(1)-localization.

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  • 04/01/2019
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