On the Strict Picard Spectrum of Commutative Ring Spectra

TL;DR

This paper computes the connective spectra of maps from integers to Picard spectra of spherical Witt vectors and the sphere spectrum, advancing understanding of their structure in algebraic topology.

Contribution

It provides explicit computations of the connective Picard spectra related to perfect rings and the sphere spectrum, revealing new structural insights.

Findings

Computed the connective spectrum of maps from ℤ to Picard spectra of spherical Witt vectors.

Determined the connective spectrum of maps from ℤ to the Picard spectrum of the sphere spectrum.

Enhanced understanding of the structure of Picard spectra in algebraic topology.

Abstract

We compute the connective spectra of maps from $\mathbb{Z}$ 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 $\mathbb{Z}$ to the Picard spectrum of the sphere spectrum.