On the Strict Picard Spectrum of Commutative Ring Spectra

2022/08/05 by Shachar Carmeli, Carmeli, Shachar · 4 citations
Mathematics · #14C22 (Secondary) #55P43 (Primary) 55P42 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2208.03073

openalex publication_date 2022/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the connective spectra of maps from ℤ to the Picard spectra of the spherical Witt vectors associated with perfect rings of characteristic p. As an application, we determine the connective spectrum of maps from ℤ to the Picard spectrum of the sphere spectrum.

Cited by

• Carlsson's Conjecture and the Generalized Total Rank Conjecture in Characteristic Two
• Tate-valued Characteristic Classes II: Applications
• K(1)-local K-theory of Azumaya algebras
• Reduced points of 𝔼_∞-rings in positive characteristic

Related

• Commutative ring spectra
• THH(Z) and the image of J
• Witt Vectors and Equivariant Ring Spectra
• Picard groups of quotient ring spectra
• An Alternative to Spherical Witt Vectors