The cohomology of Monsky and Washnitzer
The cohomology of Monsky and Washnitzer
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Monsky 和 Washnitzer 的上同调
DOI：
10.24033/msmf.324
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发表时间：
1986
影响因子：
1.9
通讯作者：
M. Put
中科院分区：
文献类型：
--
作者：
M. Put
有限域上的代数簇的Zeta函数可以用作用在该簇的p-adic上同调群上的Frobenius算子来表示。在B工作的基础上，得到了这些上同调群。Dwork的上同调称为Monsky-Washnitzer上同调。本文的前四部分对Monsky和Washnitzer的论文进行了综述。他们的工作是简化和略有扩展的使用af阿廷近似和一些刚性分析。在第5节的连接与Dwork的工作表明，阿道夫森的指数定理是在一个不同的形式在第6节。第七节详细证明了Dwork关于椭圆曲线单位根的显着公式以及参数为1/2，1/2，1的超几何微分方程解的性质。
The Zeta-function of an algebraic variety over a finite field can be expressed in terms of a Frobenius operator acting on p-adic cohomology groups of this variety. Those cohomology groups, based on work of B. Dwork, are called the Monsky-Washnitzer cohomology. The first four sections of this paper give a survey of the papers of Monsky and Washnitzer. Their work is simplified and slightly extended by the use af Artin-approximation and some rigid analysis. In section 5 the connection with Dwork's work is indicated, Adolphson's index theorem is given in a different form in section 6. Dwork's remarkable formula for the unit root of an elliptic curve and properties of the solutions of the hypergeometric differential equation with parameters ½, ½, 1 are proved in detail in section 7.