ONE POSITIVE AND TWO NEGATIVE RESULTS FOR DERIVED CATEGORIES OF ALGEBRAIC STACKS. (22nd January 2018)

• Record Type: Journal Article
• Authors: Hall, Jack; Neeman, Amnon; Rydh, David
• Is Part Of: Journal of the Institute of Mathematics of Jussieu. Volume 18:Number 5(2019)
• Page Start: 1087
• Page End: 1111
• Publication Date: 2018-01-22
• Subjects: Primary 14F05, -- Secondary 13D09, -- 14A20, -- 18G10; derived categories, -- algebraic stacks; Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S1474748017000366
• Languages: English
• ISSNs: 1474-7480

Abstract

Abstract : Let $X$ be a quasi-compact and quasi-separated scheme. There are two fundamental and pervasive facts about the unbounded derived category of $X$ : (1) $\mathsf{D}_{\text{qc}}(X)$ is compactly generated by perfect complexes and (2) if $X$ is noetherian or has affine diagonal, then the functor $\unicode[STIX]{x1D6F9}_{X}:\mathsf{D}(\mathsf{QCoh}(X))\rightarrow \mathsf{D}_{\text{qc}}(X)$ is an equivalence. Our main results are that for algebraic stacks in positive characteristic, the assertions (1) and (2) are typically false.