高层次上的滤过Poincaré引理（及其在代数群中的应用）
The filtered Poincaré lemma in higher level (with applications to algebraic groups)
摘要：
我们表明，庞加莱引理，我们证明了在其他地方的上下文中的结晶上同调的更高的水平表现良好的霍奇过滤。这使我们能够证明水平m的横向晶体的庞加莱引理。我们解释的德拉姆复杂的Berthelot-Lieberman建设，并展示了如何相同的建设可以用来研究余正规复杂的和不变的微分形式的更高水平的一组计划。把这两个实例的建设，我们表明，横向晶体的晶体扩展的代数群可以计算减少过滤德拉姆复合物。我们的理论并不忽略挠率，而且与经典的（m=0）理论不同，并非所有的封闭形式都是不变的。因此，密切不变的微分形式的水平m提供了新的不变量，我们展示了一些应用的例子。
英文摘要：
We show that the Poincaré lemma we proved elsewhere in the context of crystalline cohomology of higher level behaves well with regard to the Hodge filtration. This allows us to prove the Poincaré lemma for transversal crystals of level m. We interpret the de Rham complex in terms of what we call the Berthelot-Lieberman construction, and show how the same construction can be used to study the conormal complex and invariant differential forms of higher level for a group scheme. Bringing together both instances of the construction, we show that crystalline extensions of transversal crystals by algebraic groups can be computed by reduction to the filtered de Rham complexes. Our theory does not ignore torsion and, unlike in the classical (m=0), not all closed forms are invariant. Therefore, close invariant differential forms of level m provide new invariants and we exhibit some examples as applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
