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arXiv · 2608.09426

On the circle-equivariant cellular Tate filtration

Toni Annala·Piotr Pstrągowski
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Abstract

Using an argument of Jacob Lurie, we prove the existence of a E_2-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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Toni Annala, Piotr Pstrągowski. 2026-08-10. On the circle-equivariant cellular Tate filtration. https://arxiv.org/abs/2608.09426

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