Algebraic theories of power operations

2021/08/15 by William Balderrama, Balderrama, William · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2108.06802

openalex publication_date 2021/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop and exposit some general algebra useful for working with certain algebraic structures that arise in stable homotopy theory, such as those encoding well-behaved theories of power operations for 𝔼_∞ ring spectra. In particular, we consider Quillen cohomology in the context of algebras over algebraic theories, plethories, and Koszul resolutions for algebras over additive theories. By combining this general algebra with obstruction-theoretic machinery, we obtain tools for computing with 𝔼_∞ algebras over \mathbbF_p and over Lubin-Tate spectra. As an application, we demonstrate the existence of 𝔼_∞ periodic complex orientations at heights h≤ 2.

Cited by

• Tate-valued Characteristic Classes II: Applications
• p-adic congruences in iterated derivatives of the Weierstrass elliptic function

Related

• Level structures and cyclic power operations on the homology of 𝔼_∞ spaces
• Stable power operations
• Lubin-Tate theory, character theory, and power operations
• Cohomology theories for highly structured ring spectra
• Power operations and coactions in highly commutative homology theories