论文标题
单型方案的重建定理
Reconstruction theorem for monoid schemes
论文作者
论文摘要
我们的目标是从上面的准共束带中重建一个单体方案$ x $。这在Gabriel的原始重建定理中很重要。在$ x $的一些有限条件下，我们表明，$ x $上的Quasi-Coherent Sheaves的Topos $ \ Mathfrak的本地子类别是$ x $的一对一的，与$ x $相对应，而$ x $的元素对应于$ x $，而$ x $的元素则对应于$ topos $ $ \ math。这使我们可以从$ \ mathfrak {qc}（x）$重建$ x $。
We aim to reconstruct a monoid scheme $X$ from the category of quasi-coherent sheaves over it. This is much in the vein of Gabriel's original reconstruction theorem. Under some finiteness condition on a monoid schemes $X$, we show that the localising subcategories of the topos $\mathfrak{Qc}(X)$ of quasi-coherent sheaves on $X$ is in a one-to-one correspondence with open subsets of $X$, while the elements of $X$ correspond to the topos points of $\mathfrak{Qc}(X)$. This allows us to reconstruct $X$ from $\mathfrak{Qc}(X)$.
