Commutativity conditions for truncated Brown-Peterson spectra of height 2

TL;DR

This paper establishes algebraic conditions based on power operations that determine when truncated Brown-Peterson spectra of height 2 can exist uniquely as E_-ring spectra, with an example at prime 2.

Contribution

It provides a new algebraic criterion for the existence and uniqueness of height 2 truncated Brown-Peterson spectra as E_-ring spectra, verified in a specific prime case.

Findings

Criterion based on power operations for existence and uniqueness

Verification of the criterion at prime 2 for a specific elliptic curve example

Advances understanding of structured ring spectra in algebraic topology

Abstract

An algebraic criterion, in terms of closure under power operations, is determined for the existence and uniqueness of generalized trun- cated Brown-Peterson spectra of height 2 as E_\infty-ring spectra. The criterion is checked for an example at the prime 2 derived from the universal elliptic curve equipped with a level \Gamma_1(3)-structure.