Study of the local Langlands conjecture and the trace formula

朗兰兹猜想是对数论中一个非常重要的理论——类场论的推广。其中一部分是局部朗兰兹猜想，其GL(n)情况已被Harris、Taylor和Henniart证明。在本文中，我们证明了SL(n)在一个精确公式中的内形式的局部Langlands猜想。此外，我们把这个猜想发展到一个新的方向，并得到了一些不变量关系的结果，这些结果还没有被澄清。

The Langlands conjecture is a generalization of the class field theory, which is a very important theory in number theory.Part of it is the local Langlands conjecture, whose GL(n) case had been proved by Harris, Taylor and Henniart.In this study, we proved the local Langlands conjecture for the inner forms of SL(n) in a precise formulation.Moreover we developped the conjecture to a new direction and obtained results on relations of invariants, that was not cleared.