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arXiv · 2012.02137

Derived equivalences of gerbey curves

Soumya Sankar·Libby Taylor
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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 $C'=Pic^d(C)$, is $C=Pic^f(C')$ for some integer $f$? If $C'=Pic^d(C)$ and $C''=Pic^f(C')$, then is $C''=Pic^g(C)$ for some integer $g$?

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Soumya Sankar, Libby Taylor. 2020-12-03. Derived equivalences of gerbey curves. https://arxiv.org/abs/2012.02137

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