@article{a8e895bb4ef84e2ebac75759e66abcfe,
title = "On graded E∞ -rings and projective schemes in spectral algebraic geometry",
abstract = "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.",
keywords = "Graded E-ring, Projective scheme, Quasi-coherent sheaf, Spectral algebraic geometry",
author = "Mariko Ohara and Takeshi Torii",
note = "Funding Information: Takeshi Torii was partially supported by JSPS KAKENHI Grant Number JP17K05253. Funding Information: The first author would like to express her thanks to Professor David Gepner for his valuable advice on grading. She also would like to express her thanks to Professor Gon{\c c}alo Tabuada for a lot of advice. She had an opportunity to talk with them during a program “K -theory and related fields” at Hausdorff Institute in Bonn. The authors would like to thank the anonymous referee for useful suggestion of including Remarks 5.24. 5.26 , and 5.27. Publisher Copyright: {\textcopyright} 2021, Tbilisi Centre for Mathematical Sciences.",
year = "2022",
month = mar,
doi = "10.1007/s40062-021-00298-0",
language = "English",
volume = "17",
pages = "105--144",
journal = "Journal of Homotopy and Related Structures",
issn = "2193-8407",
publisher = "Springer Science + Business Media",
number = "1",
}