Study of various aspects of Galois representations

我们得到了几个有用的结果伽罗瓦表示。特别地，对于具有不完全剩余域的完备离散赋值域的几何Galois表示，在适当的条件下，证明了其在基域的“大”库默扩张上的固定子空间是平凡的，并将其应用于岩泽理论.此外，我们还研究了Galois表示的同余，得到了Rasmussen-Tamagawa猜想的推广结果。

We obtained several useful results on Galois representations. In particular, for a geometric Galois representation of a complete discrete valuation fields with imperfect residue field, we proved, under suitable conditions, that its fixed subspace over a ``large'' Kummer extension of the base field is trivial, and applied this to Iwasawa Theory. Moreover, we studied the congruence of Galois representations and obtained some results on the generalization of the Rasmussen-Tamagawa conjecture.