ONE POSITIVE and TWO NEGATIVE RESULTS for DERIVED CATEGORIES of ALGEBRAIC STACKS

Jack Hall; Amnon Neeman; David Rydh

doi:10.1017/S1474748017000366

ONE POSITIVE and TWO NEGATIVE RESULTS for DERIVED CATEGORIES of ALGEBRAIC STACKS

Jack Hall, Amnon Neeman, David Rydh

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

Let be a quasi-compact and quasi-separated scheme. There are two fundamental and pervasive facts about the unbounded derived category of X: (1) D_qc(X) is compactly generated by perfect complexes and (2) if X is noetherian or has affine diagonal, then the functor ψ_X: D(QCoh(X)) → D_qc(X) is an equivalence. Our main results are that for algebraic stacks in positive characteristic, the assertions (1) and (2) are typically false.

Original language	English (US)
Pages (from-to)	1087-1111
Number of pages	25
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	18
Issue number	5
DOIs	https://doi.org/10.1017/S1474748017000366
State	Published - Sep 1 2019
Externally published	Yes

Keywords

algebraic stacks
derived categories

ASJC Scopus subject areas

General Mathematics

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10.1017/S1474748017000366

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abstract = "Let be a quasi-compact and quasi-separated scheme. There are two fundamental and pervasive facts about the unbounded derived category of X: (1) Dqc(X) is compactly generated by perfect complexes and (2) if X is noetherian or has affine diagonal, then the functor ψX: D(QCoh(X)) → Dqc(X) is an equivalence. Our main results are that for algebraic stacks in positive characteristic, the assertions (1) and (2) are typically false.",

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AU - Neeman, Amnon

AU - Rydh, David

PY - 2019/9/1

Y1 - 2019/9/1

N2 - Let be a quasi-compact and quasi-separated scheme. There are two fundamental and pervasive facts about the unbounded derived category of X: (1) Dqc(X) is compactly generated by perfect complexes and (2) if X is noetherian or has affine diagonal, then the functor ψX: D(QCoh(X)) → Dqc(X) is an equivalence. Our main results are that for algebraic stacks in positive characteristic, the assertions (1) and (2) are typically false.

AB - Let be a quasi-compact and quasi-separated scheme. There are two fundamental and pervasive facts about the unbounded derived category of X: (1) Dqc(X) is compactly generated by perfect complexes and (2) if X is noetherian or has affine diagonal, then the functor ψX: D(QCoh(X)) → Dqc(X) is an equivalence. Our main results are that for algebraic stacks in positive characteristic, the assertions (1) and (2) are typically false.

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ONE POSITIVE and TWO NEGATIVE RESULTS for DERIVED CATEGORIES of ALGEBRAIC STACKS

Abstract

Keywords

ASJC Scopus subject areas

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