On normed 𝔼_∞-rings in genuine equivariant C_p-spectra

2023/08/30 by Lucy Yang, Yang, Lucy
Mathematics · #55P43 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2308.16107

openalex publication_date 2023/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Genuine equivariant homotopy theory is equipped with a multitude of coherently commutative multiplication structures generalizing the classical notion of an 𝔼_∞-algebra. In this paper we study the C_p-𝔼_∞-algebras of Nardin--Shah with respect to a cyclic group C_p of prime power order. We show that many of the higher coherences inherent to the definition of parametrized algebras collapse; in particular, they may be described more simply and conceptually in terms of ordinary 𝔼_∞-algebras as a diagram category which we call normed algebras. Our main result provides a relatively straightforward criterion for identifying C_p-𝔼_∞-algebra structures. We visit some applications of our result to real motivic invariants.

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