Maps between spherical group rings
Shachar Carmeli, Thomas Nikolaus, Allen Yuan

TL;DR
This paper characterizes the space of $ ext{E}_ infty$-ring maps between spherical group rings of finitely generated abelian groups, showing it corresponds exactly to group homomorphisms, and extends results to other ring spectra.
Contribution
It establishes a precise correspondence between $ ext{E}_ infty$-ring maps and group homomorphisms for spherical group rings, and generalizes to other spectra like $p$-groups and chromatically complete rings.
Findings
The space of $ ext{E}_ infty$-ring maps between $ ext{S}[A]$ and $ ext{S}[B]$ is discrete and corresponds to group homomorphisms.
Provides a formula for strict units in group rings of finite $p$-groups over $p$-complete spectra.
Extends the understanding of maps between ring spectra beyond classical cases.
Abstract
We prove that for finitely generated abelian groups and , the space of -ring maps between the spherical groups rings is equivalent to the discrete set of group homomorphisms . We also prove generalizations where the sphere is replaced by other ring spectra, e.g. we give a formula for the strict units in group rings of the form for a finite -group and -completely chromatically complete.
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Taxonomy
TopicsAdvanced Topics in Algebra
