The structure of the Bousfield lattice
Abstract
Using Ohkawa's theorem that the collection of Bousfield classes is a set, we perform a number of constructions with Bousfield classes. In particular, we describe a greatest lower bound operator; we also note that a certain subset DL of the Bousfield lattice is a frame, and we examine some consequences of this observation. We make several conjectures about the structure of the Bousfield lattice and DL. In particular, we conjecture that DL is obtained by killing "strange" spectra, such as the BrownComenetz dual of the sphere. We introduce a new "Boolean algebra of spectra" cBA, which contains Bousfield's BA and is complete. Our conjectures allow us to identify cBA as being isomorphic to the complete atomic Boolean algebra on {K(n) : n>= 0}, {A(n) : n>= 2}, and HF_p. Our conjectures imply that BA is the subBoolean algebra consisting of finite wedges of the K(n) and A(n), and their complements.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 1998
 DOI:
 10.48550/arXiv.math/9801103
 arXiv:
 arXiv:math/9801103
 Bibcode:
 1998math......1103H
 Keywords:

 Algebraic Topology;
 55P42;
 55P60;
 06D10
 EPrint:
 22 pages