Algebraic extensions of an Eilenberg-MacLane spectrum
Stanislaw Betley
TL;DR
This paper investigates whether certain algebraic extensions of Eilenberg-MacLane spectra remain within the same class, providing a complete answer for Galois extensions and partial results for separable and etale extensions.
Contribution
It offers a comprehensive characterization of Galois extensions of Eilenberg-MacLane spectra and partial insights into separable and etale cases.
Findings
Galois extensions of Eilenberg-MacLane spectra are always Eilenberg-MacLane spectra.
Separable and etale extensions are Eilenberg-MacLane spectra under additional conditions.
Provides criteria to identify when extensions preserve the Eilenberg-MacLane structure.
Abstract
The paper gives an answer to the question whether the Galois, separable or etale extension of an Eilenberg-MacLane spectrum in the category of ring spectra is again an Eilenberg-MacLane spectrum. We get a full answer in the Galois case. The question in separable and etale cases is answered only under additional hypothesis.
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Taxonomy
TopicsConstraint Satisfaction and Optimization · Homotopy and Cohomology in Algebraic Topology