Vinogradov C-谱序列的有穷级形式
Finite order formulation of Vinogradov's C-spectral sequence
摘要：
C-谱序列是由维诺格拉多夫在70年代后期引入的，作为研究喷流空间和微分方程的代数几何性质的基本工具。一个谱序列产生于纤维的喷射空间（或微分方程）上的形式模的接触过滤。为了避免严重的技术困难，喷射空间的顺序不是固定的，即。例如，计算是在包含任意阶jet空间的形式的空间上进行的。本文证明了在流形的有穷级jet空间中存在Vinogradov C-谱序列的一个公式。我们计算了有穷级C-谱序列的所有上同调群。得到了一个与Krupka的有穷级变分序列自然同构的有穷级变分序列.
英文摘要：
The C-spectral sequence was introduced by Vinogradov in the late Seventies as a fundamental tool for the study of algebro-geometric properties of jet spaces and differential equations. A spectral sequence arise from the contact filtration of the modules of forms on jet spaces of a fibring (or on a differential equation). In order to avoid serious technical difficulties, the order of the jet space is not fixed, i. e., computations are performed on spaces containing forms on jet spaces of any order. In this paper we show that there exists a formulation of Vinogradov's C-spectral sequence in the case of finite order jet spaces of a fibred manifold. We compute all cohomology groups of the finite order C-spectral sequence. We obtain a finite order variational sequence which is shown to be naturally isomorphic with Krupka's finite order variational sequence.
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