Cardinal continuity for cohomology theories follows from supercompact cardinals
Cardinal continuity for cohomology theories follows from supercompact cardinals
We prove that, if sufficiently large supercompact cardinals exist, then Margolis’s cardinal continuity condition holds for cohomological functors on spectra. This provides a new proof of the fact that localizations of spectra with respect to generalized cohomology theories exist, assuming the existence of a proper class of supercompact cardinals. Whether or not the existence of cohomological localizations of spectra can be proved in ZFC is a long-standing open question.
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2025, Director: Carles Casacuberta Vergés
- University of Barcelona Spain
Lògica matemàtica, Categories (Matemàtica), Mathematical logic, Cardinal numbers, Bachelor's theses, Nombres cardinals, Treballs de fi de grau, Aran Garreta Cutrina, Set theory, Topologia algebraica, Categories (Mathematics), Algebraic topology, Teoria de conjunts
Lògica matemàtica, Categories (Matemàtica), Mathematical logic, Cardinal numbers, Bachelor's theses, Nombres cardinals, Treballs de fi de grau, Aran Garreta Cutrina, Set theory, Topologia algebraica, Categories (Mathematics), Algebraic topology, Teoria de conjunts
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