The geometry of filtrations

We display a symmetric monoidal equivalence between the stable \(\infty\)-category of filtered spectra, and quasi-coherent sheaves on \(\mathbb{A}^1 / \mathbb{G}_m\), the quotient in the setting of spectral algebraic geometry, of the flat affine line by the canonical action of the flat multiplicativ...

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Bibliographic Details
Published in:arXiv.org 2021-07
Main Author: Moulinos, Tasos
Format: Article
Language:English
Subjects:
Quotients
Sheaves
Online Access:Get full text
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Summary:We display a symmetric monoidal equivalence between the stable \(\infty\)-category of filtered spectra, and quasi-coherent sheaves on \(\mathbb{A}^1 / \mathbb{G}_m\), the quotient in the setting of spectral algebraic geometry, of the flat affine line by the canonical action of the flat multiplicative group scheme. Via a Tannaka duality argument, we identify the underlying spectrum and associated graded functors with pull-backs of quasi-coherent sheaves along certain morphisms of stacks.
ISSN:2331-8422
DOI:10.48550/arxiv.1907.13562