https://rochester.zoom.us/j/6775967436

In this talk, we will discuss a lifting problem for modules over subalgebras of the Steenrod algebra, along with how this problem relates to computations of localized Ext groups. In general, for any algebra, A, and some subalgebra, B, one can ask which B-modules can be lifted to A-modules. (That is, can be given an A-module structure in a way that is compatible with the existing B-module structure.) We will consider this problem in the case where A is the Steenrod algebra.

The Steenrod algebra is filtered by a family of subalgebras, A(n) for each nonnegative integer, n. This gives a gradation of the lifting problem–if an A(n)-module fails to lift to an A-module, we can ask how far up the filtration the module does lift (i.e., what is the largest m so that the A(n)-module lifts to an A(m)-module). We will focus on criteria for lifting A(1)-modules. In particular, we will discuss an application of a spectral sequence of Davis and Mahowald to this lifting problem, which connects the question to one regarding localized Ext groups. Along the way, we will explore the stable category of A(1)-modules and the utility of Margolis homology in this context.