$ \newcommand\A{\mathrm{A}} \newcommand\E{\mathrm{E}} \newcommand\G{\mathrm{G}} \newcommand\H{\mathrm{H}} \newcommand\K{\mathrm{K}} \newcommand\L{\mathrm{L}} \newcommand\M{\mathrm{M}} \newcommand\Ascr{\mathcal{A}} \newcommand\Cscr{\mathcal{C}} \newcommand\Dscr{\mathcal{D}} \newcommand\Escr{\mathcal{E}} \newcommand\Kscr{\mathcal{K}} \newcommand\Perfscr{\mathcal{P}\mathrm{erf}} \newcommand\Acscr{\mathcal{A}\mathrm{c}} \newcommand\heart{\heartsuit} \newcommand\cn{\mathrm{cn}} \newcommand\op{\mathrm{op}} \newcommand\Ho{\mathrm{Ho}} \newcommand\dR{\mathrm{dR}} \newcommand\HH{\mathrm{HH}} \newcommand\TC{\mathrm{TC}} \newcommand\ku{\mathrm{ku}} \newcommand{\bMap}{\mathbf{Map}} \newcommand{\End}{\mathrm{End}} \newcommand{\Mod}{\mathrm{Mod}} \newcommand\bE{\mathbf{E}} \newcommand\bZ{\mathbf{Z}} \newcommand\bAM{\mathbf{AM}} \newcommand\bLM{\mathbf{LM}} \newcommand\Spec{\mathrm{Spec}} \newcommand\we{\simeq} \newcommand\qc{\mathrm{qc}} $

I have posted two Oberwolfach Reports ([1] and [2]) from this year, one on the even filtration of Hahn–Raksit–Wilson [3] and one on forthcoming work of my own on filtered derived commutative rings. The first report serves as my arXiv review of Hahn–Raksit–Wilson, although I wrote it before it appeared on the arXiv and I do not discuss their application of the even filtration to $\TC$ of the Adams summand of $\ku$. Basically, the even filtration is a big deal.


[1] Antieau, The even filtration after Hahn, Raksit, and Wilson, Oberwolfach Report 24/2022.

[2] Antieau, What is de Rham cohomology?, Oberwolfach Report 35/2022.

[3] Hahn, Raksit, and Wilson, A motivic filtration on the topological cyclic homology of commutative ring spectra, arXiv:2206.11208.