F. Luke Wolcott | Searcharxiv

arXiv2014

Bousfield lattices of non-Noetherian rings: some quotients and products

In the context of a well generated tensor triangulated category, Section 3 investigates the relationship between the Bousfield lattice of a quotient and quotients of the Bousfield lattice. In Section 4 we develop a general framework to study the Bousfield lattice of the derived category of a commutative or graded-commutative ring, using derived functors induced by extension of scalars. Section 5 applies this work to extend results of Dwyer and Palmieri [DP08] to new non-Noetherian rings.

math.AT↗

arXiv2014

Variations of the telescope conjecture and Bousfield lattices for localized categories of spectra

We investigate several versions of the telescope conjecture on localized categories of spectra, and implications between them. Generalizing the "finite localization" construction, we show that on such categories, localizing away from a set of strongly dualizable objects is smashing. We classify all smashing localizations on the harmonic category, HFp-local category and I-local category, where I is the Brown-Comenetz dual of the sphere spectrum; all are localizations away from strongly dualizable objects, although these categories have no nonzero compact objects. The Bousfield lattices of the harmonic, E(n)-local, K(n)-local, HFp-local and I-local categories are described, along with some lattice maps between them. One consequence is that in none of these categories is there a nonzero object that squares to zero. Another is that the HFp-local category has localizing subcategories that are not Bousfield classes.

math.AT↗

arXiv2012

Not every object in the derived category of a ring is Bousfield equivalent to a module

We consider the derived category of a specific non-Noetherian ring Λ, and show that there are objects in D(Λ) that are not Bousfield equivalent to any module. This answers a question posed by Dwyer and Palmieri.

math.CT↗