The geometry of filtrations

Abstract

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.

Publication version

References in corpus (2)

• A note on stable recollements
• Derived Fundamental Groups for Tate Motives

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