Finite chromatic defect implies the telescope conjecture

Let EE be a spectrum with finite chromatic defect, meaning that its chromatic defect is finite. The telescope conjecture is the assertion that the relevant finite-height telescope localization agrees with the corresponding finite-height monochromatic localization at each height and prime.

Finite-defect telescope conjecture. Any spectrum with finite chromatic defect satisfies the condition of the telescope conjecture at all heights and primes.

This conjecture proposes that finite chromatic defect forces the telescope conjecture uniformly across all chromatic heights and primes. The source gives no resolution or partial result establishing the assertion in general.

Sources & referencesView supporting material

Primary source

Christian Carrick, “Chromatic defect, Wood's theorem, and higher real K-theories”, arXiv:2402.17519 (2025).

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