论文标题
属于Abelian品种的属曲线的派生类别
Derived categories of curves of genus one and torsors over abelian varieties
论文作者
论文摘要
假设$ c $是完美的字段$ f $上的属1属的光滑投射曲线，而$ e $是其雅各布。如果$ c $没有$ f $ - 合理的积分，那么$ c $和$ e $不是同构的，$ c $是$ e $ - torsor，带有$δ（c）\ in H^1（\ text {gal}（\ bar f/f）（\ bar f/f），e（\ bar f））$。然后，$δ（c）$确定\ text {br}（e）/\ text {br}（f）$的类$β\，并且在（扭曲的）相干吊羊$ \ Mathcal d（c）\ xrightArrow {c right xrightArrow {\ gancal} $ n（e）$ n（e）$ arcalcal d（c）$ arc）$（e）（e）（e）（e）（e）（e）（e）（e）（e）我们将此结果推广到更高的维度；也就是说，我们也证明了这是针对阿伯利亚品种的扭转。
Suppose $C$ is a smooth projective curve of genus 1 over a perfect field $F$, and $E$ is its Jacobian. In the case that $C$ has no $F$-rational points, so that $C$ and $E$ are not isomorphic, $C$ is an $E$-torsor with a class $δ(C)\in H^1(\text{Gal}(\bar F/F), E(\bar F))$. Then $δ(C)$ determines a class $β\in \text{Br}(E)/\text{Br}(F)$ and there is a Fourier-Mukai equivalence of derived categories of (twisted) coherent sheaves $\mathcal D(C) \xrightarrow{\cong} \mathcal D(E, β^{-1})$. We generalize this result to higher dimensions; namely, we prove it also for torsors over abelian varieties.
