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- W4288795526 abstract "In this work we study the $E_{infty}$-ring $text{THH}(mathbb{F}_p)$ as a graded spectrum. Following an identification at the level of $E_2$-algebras with $mathbb{F}_p[Omega S^3]$, the group ring of the $E_1$-group $Omega S^3$ over $mathbb{F}_p$, we show that the grading on $text{THH}(mathbb{F}_p)$ arises from decomposition on the cyclic bar construction of the pointed monoid $Omega S^3$. This allows us to use trace methods to compute the algebraic $K$-theory of $text{THH}(mathbb{F}_p)$. We also show that as an $E_2$ $Hmathbb{F}_p$-ring, $text{THH}(mathbb{F}_p)$ is uniquely determined by its homotopy groups. These results hold in fact for $text{THH}(k)$, 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." @default.
- W4288795526 created "2022-07-30" @default.
- W4288795526 creator A5020442037 @default.
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- W4288795526 date "2020-09-12" @default.
- W4288795526 modified "2023-09-29" @default.
- W4288795526 title "Algebraic $K$-theory of $text{THH}(mathbb{F}_p)$" @default.
- W4288795526 doi "https://doi.org/10.48550/arxiv.2009.05827" @default.
- W4288795526 hasPublicationYear "2020" @default.
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