On the study of cohomology of Chevalley groups using the etale cohomology thoery

确定有限Chvalley群(分类空间)的上同调，包括以下几个方面：(1)利用代数几何的概念，构造收敛于有限Chvalley群(分类空间)上同调的谱序列：(2)构造一个给出谱序列的第二项的复形；(3)证明了谱序列的平凡性。对于(1)，我们利用Eilenberg-Moore谱序列的代数形式Deligne谱序列，成功地构造了收敛于Borel构造模型的单纯格式的谱序列。此外，我们用Hochschild谱序列来表示上述谱序列的平凡，从而成功地得到了上述谱序列。对于(2)，我们构造了具体的复形，对于所有自旋或类型和例外类型的情况，都给出了谱序列的第二项我们通过在谱序列中引入一些上同调运算来表示谱序列的平凡，这可能需要在未来进行更多的研究。

The research project is to determine the cohomology of (the classifying space of) finite Chevalley groups, which consists of the following.(1) to construct, using the notion of algebraic geometry, the spectral sequence converging to the cohomology of (the classifying space of) finite Chevalley groups ;(2) to construct a complex giving the second term of the spectral sequence ;(3) to show the triviality of the spectral sequence.As for (1), we have succeeded in constructing the spectral sequence converging to the simplicial scheme which is the model of the Borel construction, by using the Deligne spectral sequence which is the algebraic version of the Eilenberg-Moore spectral sequence.Furthermore we use the Hochschild spectral sequence to show the triviality of the above spectral sequence, and thus we have succeeded in obtaining the spectral sequence mentioned in the above.As for (2), we have constructed concretely complexes giving the second term of the spectral sequence for all the cases of spinor type and of exceptional type.Finally, as for (3), we have some ideas to show the triviality of the spectral sequence by introducing some cohomology operations into the spectral sequence, which may need some more studies in the future.