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 \(\text { {Proj}}\,(A)\) associated to a connective \({\mathbb {N}}\)-graded \({\mathbb {E}}_{\infty }\)-ring A can be described in terms of \({{\mathbb {Z}}}\)-graded A-modules.

我们引入了分级\({\mathbb {E}}_{\infty }\)环和分级模块，并研究了它们的性质。我们构建了与谱代数几何中的联结\({\mathbb {N}}\)分级\({\mathbb {E}}_{\infty }\)环相关的射影方案。在某些有限性条件下，我们证明了与连接词相关联的谱射影方案\ (\text { {Proj}}\,(A)\)上几乎完美的准相干滑轮的\(\infty \)类别({\mathbb {N}}\) -分级\({\mathbb {E}}_{\infty }\) -环A可以用\({{\mathbb {Z}}}\)来描述-A级模块。