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Transchromatic phenomena in the equivariant slice spectral sequence

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arxiv 2403.00741 v1 pith:2JWCC6OK submitted 2024-03-01 math.AT

classification math.AT
keywords theoriestranschromaticequivariantheight-phenomenonproveslicespectral
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abstract

In this paper, we prove a transchromatic phenomenon for Hill--Hopkins--Ravenel and Lubin--Tate theories. This establishes a direct relationship between the equivariant slice spectral sequences of height-$h$ and height-$(h/2)$ theories. As applications of this transchromatic phenomenon, we prove periodicity and vanishing line results for these theories.

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  1. On higher real $K$-theories and finite spectra

    math.KT 2025-07 conditional novelty 8.0 of 10

    At the prime 2, the connective higher real K-theories eo_h are shown to be fp spectra of type h, which implies a divisibility constraint on Euler characteristics and a new obstruction to generalized Moore spectra.

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