In this note, we give a brief overview of the telescope conjecture and the chromatic splitting conjecture in stable homotopy theory. In particular, we provide a proof of the folklore result that Ravenel’s telescope conjecture for all heights combined is equivalent to the generalized telescope conjecture for the stable homotopy category, and explain some similarities with modular representation theory.
CITATION STYLE
Barthel, T. (2020). A short introduction to the telescope and chromatic splitting conjectures. In Springer Proceedings in Mathematics and Statistics (Vol. 309, pp. 261–273). Springer. https://doi.org/10.1007/978-981-15-1588-0_9
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