The geometry of filtrations
We display a symmetric monoidal equivalence between the stable ∞ ‐category of filtered spectra, and quasi‐coherent sheaves on A1/Gm , 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.