Unstable Modules with Only the Top k Steenrod Operations

We study an abelian category of unstable modules with the top k Steenrod operations at the prime 2. We show that this category has homological dimension at most k. We establish forgetful functors, suspension functors, loop functors and Frobenius functors between such modules. The forgetful functors induce an inverse system of Ext groups, and the inverse system stabilizes when the covariant module is bounded above. We define an analogue of the Lambda algebra in this context and verify that its cohomology computes Ext.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2021

Author dc:creator

• Li, Zhulin

Advisor dc:contributor.advisor

• Miller, Haynes R.

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright MIT

Licence dc:rights.uri

• http://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/139023

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/139023