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

Jack Hall, Amnon Neeman, David Rydh

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1087-1111
Number of pages25
JournalJournal of the Institute of Mathematics of Jussieu
Volume18
Issue number5
DOIs
StatePublished - Sep 1 2019

Keywords

  • algebraic stacks
  • derived categories

ASJC Scopus subject areas

  • Mathematics(all)

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