ONE POSITIVE AND TWO NEGATIVE RESULTS FOR DERIVED CATEGORIES OF ALGEBRAIC STACKS
Jack Hall, Amnon Neeman, David Rydh
JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU | CAMBRIDGE UNIV PRESS | Published : 2019
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.
Awarded by Australian Research Council (ARC)
Awarded by Swedish Research Council (VR)
The first and second author are supported by the Australian Research Council (ARC), grant numbers FL100100137, DE150101799, and DP150102313. The third author is supported by the Swedish Research Council (VR), grant numbers 2011-5599 and 2015-05554.