Equivalences of derived categories of sheaves on tame stacks

2024/05/30 by Fei Peng, Peng, Fei
Computer Science · Mathematics · #14F08 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary 14F06 #Secondary 14A20

paper · pdf · doi:10.48550/arxiv.2405.19676

openalex publication_date 2024/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Building on Olander's work on algebraic spaces, we prove Orlov's representability theorem relating fully faithful functors and Fourier--Mukai transforms between the bounded derived category of coherent sheaves to the case of smooth, proper, and tame algebraic stacks. This extends previous results of Kawamata for Deligne--Mumford stacks with generically trivial stabilizers and projective coarse moduli spaces.

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