On formality of diagrams of Eilenberg-MacLane spaces
Grigory Solomadin, Antoine Touz\'e

TL;DR
This paper proves that diagrams of Eilenberg-MacLane spaces are formal over the rationals, leading to spectral sequence collapse, but not over other rings, using functor calculus.
Contribution
It establishes formality over $Q$ for diagrams of Eilenberg-MacLane spaces and shows non-formality over rings not containing $Q$.
Findings
Spectral sequence over $Q$ collapses at page 2 for diagrams of EML spaces.
Formality holds over $Q$ but not over rings lacking $Q$.
Abstract
In this paper, we establish formality (over ) for diagrams of Eilenberg-MacLane spaces of any height . This implies spectral sequence (over ) collapse at page for any diagram of EML spaces over any small category. We prove by functor calculus argument that formality does not hold over any fixed commutative ring not containing , where the category of diagrams is over the category generated by finite direct sums of a cyclic group.
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