本学位论文主要研究了刚性上同调与Adolphson 和 Sperber 定义的 Dwork 上同调之间的关系。同时计算了 Dwork isocrystal 在 torus 上的刚性上同调。主要内容分以下三个部分：（1）Dwork 在证明韦伊猜想有理性部分的时候，定义了一系列的分裂函数。Adolphson 以及 Sperber 将 Dwork 的理论引入指数和的研究当中。每个分裂函数都可以定义一个 Dwork 上同调。这里比较了不同分裂函数定义的 Dwork 上同调是互相同构的。我们知道 Adolphson 和 Sperber 在指数和问题中之所以选择最复杂的分裂函数是为了计算上面的方便。本节的同构定理表明，大部分的结果都可以用最简单的分裂函数来刻画。（2）Bourgeois 证明了在一些特定的条件之下，刚性上同调和 Dwork 上同调是同构的。我们的目的是将一些多余的条件去除。我们首先给出了 Dwork 上同调中使用的函数空间在刚性上同调理论的刻画。这里的函数空间可以表达成一个仿射 toric 代数簇的第0个刚性上同调。取该仿射 toric 代数簇一个光滑的消解，会产生一个正规交叉除子。我们可以定义一个带 logarithmic 极点的复形。我们分别比较该复形和 Dwork 上同调，以及 torus 上 Dwork isocrystal 的刚性上同调。（3）Robba 计算了单变量的指数和对应 L 函数的根的赋值的估计。Adolphson 和 Sperber 在之后延拓了 Robba 的结果并且证明了 L 函数得到的牛顿折线在 Hodge 折线之上。这一部分是将 Robba 直接计算的方法推广到多变量的指数和。重新证明了Adolphson 和 Sperber的结果。并且在某些特殊的情形下，给出了两条折线重合的充要条件。

In the present paper, we give a comparison theorem between the Dwork cohomology introduced by Adolphson and Sperber and the rigid cohomology. As a corollary, we can calculate the rigid cohomology of Dwork isocrystal on torus. The main content is divided into the following three parts: （1） Dwork defined a series of splitting functions when proving that the rational part of Weil‘s conjecture. Adolphson and Sperber introduced Dwork‘s theory into the study of exponential sums. Note that each splitting function can define a kind of Dwork cohomology. Here we compare that the Dwork cohomology defined by different split functions are mutually isomorphic. We know that Adolphson and Sperber chose the most complex splitting function in the exponential sum problem for the convenience of calculation. The isomorphism theorem in this part shows that most results can be characterized by the simplest splitting function. （2） Bourgeois proved that rigid cohomology and Dwork cohomology are isomorphic under some specific conditions. Our aim is to remove these conditions. We first give a description of the function space used in Dwork cohomology. The function space can be expressed as the 0-th rigid cohomology of an affine toric variety. Take a smooth resolution of the affine toric variety, which produces a normal cross divisor. A complex with logarithmic poles can be defined. We establish a comparison theorem between this complex and the Dwork cohomology, and the rigid cohomology of the Dwork isocrystal on torus, respectively. （3） Robba computed exponential sums of one variable and obtained estimates of the roots of the $L$-function. Adolphson and Sperber extended Robba‘s results and proved that the Newton polygon lies above the Hodge polygon. This part is to generalize Robba‘s method to multivariate exponential sums. The results of Adolphson and Sperber are reproved. In some special cases, the necessary and sufficient conditions for the coincidence of two polygons are given.