08/01/2013, 11:00 — 12:00 — Sala P3.10, Pavilhão de Matemática Luke Wolcott, University of Western Ontario
Bousfield lattices, quotients, ring maps, and non-Noetherian rings
Given an object in a compactly generated tensor triangulated
category (such as the derived category of a ring, or the stable
homotopy category), the Bousfield class of is the collection of
objects that tensor with to zero. The set of Bousfield classes
forms a lattice, called the Bousfield lattice . First, we
will look at examples of when a functor induces a
lattice map , and will describe several lattice
quotients and lattice isomorphisms. Second, we will focus on
homological algebra; a ring map induces, via extension
of scalars, a functor , and this induces a map on
Bousfield lattices. Third, we specialize to a specific map between
some interesting non-Noetherian rings.
