Derived equivalences of gerbey curves
Abstract
We study derived equivalences of certain stacks over genus 1 curves, which arise as connected components of the Picard stack of a genus 1 curve. To this end, we develop a theory of integral transforms for these algebraic stacks. We use this theory to answer the question of when two stacky genus 1 curves are derived equivalent. We use integral transforms and intersection theory on stacks to answer the following questions: if C'=Picd(C), is C=Picf(C') for some integer f? If C'=Picd(C) and C''=Picf(C'), then is C''=Picg(C) for some integer g?
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