Representability of derived stacks
Representability of derived stacks
复制标题
DOI：
10.1017/is012001005jkt179
复制
发表时间：
2010-11
期刊：
影响因子：
--
通讯作者：
J.P.Pridham
中科院分区：
文献类型：
--
作者：
J.P.Pridham
Lurie的可表示性定理给出了函子是几乎有限表示的派生几何堆栈的充分必要条件。我们建立了Lurie定理的几个变体，使假设更容易在许多应用中验证。如果施莱辛格条件的一个导出的类似形式成立，则定理简化为在下部和上同调群上的验证条件。另一种简化是，函子只需要在离散环的幂零扩展上定义。最后，有一个预表征性定理，它可以应用于将显式几何堆栈与dg流形和相关对象联系起来。
Lurie's representability theorem gives necessary and sufficient conditions for a functor to be an almost finitely presented derived geometric stack. We establish several variants of Lurie's theorem, making the hypotheses easier to verify for many applications. Provided a derived analogue of Schlessinger's condition holds, the theorem reduces to verifying conditions on the underived part and on cohomology groups. Another simplification is that functors need only be defined on nilpotent extensions of discrete rings. Finally, there is a pre-representability theorem, which can be applied to associate explicit geometric stacks to dg-manifolds and related objects.