Abstract
Homological localizations of spaces and spectra have been a fundamental tool in algebraic topology since the 1970s, especially in the setting of chromatic homotopy. However, it is unknown whether the existence of cohomological localizations can be proved in ZFC or not. Although this is apparently a homotopy-theoretical problem, it turned out to be closely related to set-theoretical reflection principles and therefore to the existence of large cardinals. In this note we present the state of the art with enough background so that proofs of results are readable by both topologists and set theorists.
Supported by MCIN/AEI/10.13039/501100011033 under grant PID2020-117971GB-C22.
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I thank Joan Bagaria for revising and correcting the set-theoretical content of the manuscript.
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Casacuberta, C. (2023). Cohomological Localizations and Set-Theoretical Reflection. In: Morel, JM., Teissier, B. (eds) Mathematics Going Forward . Lecture Notes in Mathematics, vol 2313. Springer, Cham. https://doi.org/10.1007/978-3-031-12244-6_13
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