Unstable modules with only the top k Steenrod operations

Li, Zhulin

doi:10.2140/agt.2021.21.3623

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Unstable modules with only the top $k$ Steenrod operations

Zhulin Li

Algebraic & Geometric Topology 21 (2021) 3623–3662

DOI: 10.2140/agt.2021.21.3623

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 $Λ$ algebra in this context and verify that its cohomology computes $Ext$ .

Keywords

Steenrod algebra, ringoid, top $k$ operations

Mathematical Subject Classification

Primary: 55S10

Secondary: 55U99

References

Publication

Received: 12 July 2020

Revised: 21 December 2020

Accepted: 7 January 2021

Published: 28 December 2021

Authors

Zhulin Li
Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States

Volume 21, issue 7 (2021)