On graded E∞-rings and projective schemes in spectral algebraic geometry

We introduce graded E ∞ -rings and graded modules over them, and study their properties. We construct projective schemes associated to connective N -graded E ∞ -rings in spectral algebraic geometry. Under some finiteness conditions, we show that the ∞ -category of almost perfect quasi-coherent sheav...

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Bibliographic Details
Published inJournal of homotopy and related structures Vol. 17; no. 1; pp. 105 - 144
Main Authors Ohara, Mariko, Torii, Takeshi
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 2022
Springer Nature B.V
Subjects
Algebra
Algebraic Topology
Functional Analysis
Mathematics
Mathematics and Statistics
Modules
Number Theory
Rings (mathematics)
Sheaves
Spectra
Quasi-coherent sheaf
Graded
Spectral algebraic geometry
Projective scheme
ring
18G80
Primary 14A30 Secondary 55P43
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Summary:We introduce graded E ∞ -rings and graded modules over them, and study their properties. We construct projective schemes associated to connective N -graded E ∞ -rings in spectral algebraic geometry. Under some finiteness conditions, we show that the ∞ -category of almost perfect quasi-coherent sheaves over a spectral projective scheme Proj ( A ) associated to a connective N -graded E ∞ -ring A can be described in terms of Z -graded A -modules.
ISSN:2193-8407
1512-2891
DOI:10.1007/s40062-021-00298-0