One positive and two negative results for derived categories of algebraic stacks

2014/05/08 by Hall, Jack, Neeman, Amnon, Rydh, David · 4 citations
#14A20 #18G10 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14F05 #secondary 13D09

paper · doi:10.48550/arxiv.1405.1888

Abstract

Let X 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 \colon 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.

Cited by

• Frobenius generation for algebraic stacks
• Nonexistence of singly compactly generated t-structures for schemes
• Dualizability of derived categories of algebraic stacks
• Perfectly generated t-structures for algebraic stacks

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