2020/09/12 by Bayındır, Haldun Özgür, Moulinos, Tasos
#19D99 #55P99 #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)
paper · doi:10.48550/arxiv.2009.05827
In this work we study the E∞-ring THH(\mathbbFp) as a graded spectrum. Following an identification at the level of E2-algebras with \mathbbFp[ΩS3], the group ring of the E1-group ΩS3 over \mathbbFp, we show that the grading on THH(\mathbbFp) arises from decomposition on the cyclic bar construction of the pointed monoid ΩS3. This allows us to use trace methods to compute the algebraic K-theory of THH(\mathbbFp). We also show that as an E2 H\mathbbFp-ring, THH(\mathbbFp) is uniquely determined by its homotopy groups. These results hold in fact for THH(k), where k is any perfect field of characteristic p. Along the way we expand on some of the methods used by Hesselholt-Madsen and later by Speirs to develop certain tools to study the THH of graded ring spectra and the algebraic K-theory of formal DGAs.