On the derived functors of destabilization at odd primes

TL;DR

This paper constructs an explicit chain complex to compute derived functors of destabilization at odd primes, extending previous work and applying methods that also work at prime two, providing new structural insights.

Contribution

It introduces a new explicit chain complex for derived functors of destabilization at odd primes, generalizing prior constructions and applying Singer and Miller's ideas.

Findings

Constructed an explicit chain complex for derived functors

Generalized previous constructions by Zarati and Hung-Sum

Deduced a structural result on the derived functors

Abstract

An explicit chain complex is constructed to calculate the derived functors of destabilization at an odd prime, generalizing constructions of Zarati and of Hung and Sum. The methods are based on the ideas of Singer and Miller and also apply at the prime two. A structural result on the derived functors of destabilization is deduced.