# On a Conjecture of Mahowald on the Cohomology of Finite Sub-Hopf algebras of the Steenrod Algebra

## TL;DR

This paper proves Mahowald's conjecture, establishing the existence of specific nonzero classes in the cohomology of finite sub-Hopf algebras of the Steenrod algebra, linking algebraic structures to stable homotopy theory.

## Contribution

It provides a proof of Mahowald's conjecture, connecting cohomology classes of sub-Hopf algebras to generators in homotopy rings of periodic spectra.

## Key findings

- Confirmed the existence of nonzero classes in cohomology of A(n)
- Linked cohomology classes to generators in homotopy rings
- Supported the chromatic perspective in stable homotopy theory

## Abstract

Mahowald's conjecture arose as part of a program attempting to view chromatic phenomena in stable homotopy theory through the lens of the classical Adams spectral sequence. The conjecture predicts the existence of nonzero classes in the cohomology of the finite sub-Hopf algebras $A(n)$ of the mod 2 Steenrod algebra that correspond to generators in the homotopy rings of certain periodic spectra. The purpose of this note is to present a proof of the conjecture.