Unstable Modules with Only the Top k Steenrod Operations
Name
li-zhulin-phd-math-2021-thesis.pdf.pdf
Description
Thesis PDF
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479.96 KB
Format
Adobe PDF
Checksum (MD5)
415361e49dc0cffa5ceecf05038d1ac7
Author(s)
Li, Zhulin
Advisor(s)
Miller, Haynes R.
Date Issued
June 2021
Publisher
Massachusetts Institute of Technology
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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