2026-09-20T15:09:19Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1390232022-01-15T04:05:12Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Miller, Haynes R.
Li, Zhulin
Massachusetts Institute of Technology. Department of Mathematics
2022-01-14T14:45:14Z
2022-01-14T14:45:14Z
2021-06
2021-05-25T12:47:11.258Z
https://hdl.handle.net/1721.1/139023
https://orcid.org/0000-0003-1376-4678
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.
Ph.D.
Massachusetts Institute of Technology
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Unstable Modules with Only the Top k Steenrod Operations
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<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.</Abstract>
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