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A Short Introduction to the Telescope and Chromatic Splitting Conjectures

  • Tobias BarthelEmail author
Conference paper
  • 14 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 309)

Abstract

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.

Keywords

Bousfield localization Telescope conjecture Chromatic splitting conjecture 

Notes

Acknowledgements

I would like to thank Mike Hopkins and the participants of Talbot 2013 for several useful discussions on this topic as well as Agnès Beaudry, Malte Leip, Doug Ravenel, Gabriel Valenzuela, and the referee for comments on an earlier draft of this document. Furthermore, I am grateful to Haynes Miller and Norihiko Minami for encouraging me to revise my original talk notes.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Max Planck Institute for MathematicsBonnGermany

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