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

12 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

Access to Document

10.1017/S1474748017000366

Cite this

@article{e6a6efb94cec4a179443fe4cb2821b16,

title = "ONE POSITIVE and TWO NEGATIVE RESULTS for DERIVED CATEGORIES of ALGEBRAIC STACKS",

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.",

keywords = "algebraic stacks, derived categories",

author = "Jack Hall and Amnon Neeman and David Rydh",

note = "Publisher Copyright: {\textcopyright} 2018 Cambridge University Press.",

year = "2019",

month = sep,

day = "1",

doi = "10.1017/S1474748017000366",

language = "English (US)",

volume = "18",

pages = "1087--1111",

journal = "Journal of the Institute of Mathematics of Jussieu",

issn = "1474-7480",

publisher = "Cambridge University Press",

number = "5",

}

TY - JOUR

T1 - ONE POSITIVE and TWO NEGATIVE RESULTS for DERIVED CATEGORIES of ALGEBRAIC STACKS

AU - Hall, Jack

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.

KW - algebraic stacks

KW - derived categories

UR - http://www.scopus.com/inward/record.url?scp=85071241466&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85071241466&partnerID=8YFLogxK

U2 - 10.1017/S1474748017000366

DO - 10.1017/S1474748017000366

M3 - Article

AN - SCOPUS:85071241466

SN - 1474-7480

VL - 18

SP - 1087

EP - 1111

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

IS - 5

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this