On the circle-equivariant cellular Tate filtration
Toni Annala, Piotr Pstrągowski
Abstract
Using an argument of Jacob Lurie, we prove the existence of a E2-lax monoidal structure on the Tate filtration coming from the standard cell structure on the infinite complex projective space. We then compare it to the filtration induced by the standard t-structure on spectra. In the last part of the paper, we construct a synthetic variant of the cellular Tate filtration and use it to compare Antieau's, Bhatt-Lurie's and Raksit's HKR filtrations on negative cyclic and periodic homology.
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