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arXiv · 1803.09389

On graded $\mathbb{E}_{\infty}$-rings and projective schemes in spectral algebraic geometry

Mariko Ohara·Takeshi Torii
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Abstract

We introduce graded $\mathbb{E}_{\infty}$-rings and graded modules over them, and study their properties. We construct projective schemes associated to connective $\mathbb{N}$-graded $\mathbb{E}_{\infty}$-rings in spectral algebraic geometry. Under some finiteness conditions, we show that the $\infty$-category of almost perfect quasi-coherent sheaves over a spectral projective scheme $\mathrm{Proj}\,(A)$ associated to a connective $\mathbb{N}$-graded $\mathbb{E}_{\infty}$-ring $A$ can be described in terms of $\mathbb{Z}$-graded $A$-modules.

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Mariko Ohara, Takeshi Torii. 2018-03-26. On graded $\mathbb{E}_{\infty}$-rings and projective schemes in spectral algebraic geometry. https://arxiv.org/abs/1803.09389

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