MathDBThe Dichotomy Conjecture for finite locals and finite acyclics
The Dichotomy Conjecture for finite locals and finite acyclics
A spectrum has a finite local if some nontrivial finite spectrum is local with respect to it, and it has a finite acyclic if some nontrivial finite spectrum is annihilated by it.
The Dichotomy Conjecture. Every spectrum has either a finite local or a finite acyclic.
The source attributes this conjecture to Hovey and collaborators and states that it is equivalent to the finite-local formulation involving Bousfield classes. No resolution is given.
Sources & referencesView supporting material
Primary source
Mark Hovey and John Palmieri, “The structure of the Bousfield lattice”, arXiv:math/9801103 (1998).
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