The cellular Tate filtration is lax E2-monoidal, and the HKR filtrations of Antieau, Bhatt-Lurie, and Raksit on negative cyclic and periodic homology coincide.
Bals, Periodic cyclic homology over Q , Annals of K-Theory 9 (2024), no
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On the circle-equivariant cellular Tate filtration
The cellular Tate filtration is lax E2-monoidal, and the HKR filtrations of Antieau, Bhatt-Lurie, and Raksit on negative cyclic and periodic homology coincide.