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 language||English (US)|
|Number of pages||25|
|Journal||Journal of the Institute of Mathematics of Jussieu|
|Publication status||Published - Sep 1 2019|
- algebraic stacks
- derived categories
ASJC Scopus subject areas