A generalized Bondal-Orlov full faithfulness criterion for Deligne-Mumford stacks

2024/05/10 by Hall, Jack, Priver, Kyle · 2 citations
#14F08 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14F06 #secondary 14A20

paper · doi:10.48550/arxiv.2405.06229

Abstract

Let X, Y be smooth projective varieties over C. Let K be a bounded complex of coherent sheaves on X× Y and let Φ_K \colon D^b_Coh(X) → D^b_Coh(Y) be the resulting Fourier-Mukai functor. There is a well-known criterion due to Bondal-Orlov for Φ_K to be fully faithful. This criterion was recently extended to smooth Deligne-Mumford stacks with projective coarse moduli schemes by Lim-Polischuk. We extend this to all smooth, proper Deligne-Mumford stacks over arbitrary fields of characteristic 0. Along the way, we establish a number of foundational results for bounded derived categories of proper and tame morphisms of noetherian algebraic stacks (e.g., coherent duality).

Cited by

• Frobenius generation for algebraic stacks
• Moduli of non-pure sheaves and contractions of Hilbert schemes

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