论文标题
Gerbey曲线的派生等效性
Derived equivalences of gerbey curves
论文作者
论文摘要
我们研究了某些堆栈比属$ 1 $曲线的衍生等效性，这些曲线是作为$ 1 $曲线的Picard堆栈的连接组件而产生的。为此，我们为这些代数堆栈开发了整体变换的理论。我们使用该理论回答一个问题，即何时出现了两个二叠纪$ 1 $曲线的等效曲线。我们在堆栈上使用积分转换和交叉理论来回答以下问题：如果$ c'= pic^d（c）$，是$ c = pic^f（c'）$ f $？如果$ c'= pic^d（c）$和$ c''= pic^f（c'）$，则是$ c''= pic^g（c）$，用于某些整数$ g $？
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 $g$?
