Congruence relations between p-adic crystalline representations

设p是有理素数。在这个项目中，我研究了完全离散赋值域的p-进Galois表示之间的各种同余关系。P-进Galois表示是数论的重要研究对象。这个项目的目的是开发方法，通过使用同余关系将伽罗瓦表示的研究简化为更简单的情况。作为这一项目最重要的成果，我证明了完全离散赋值域的混合特征模分枝子群与等特征模分枝子群的绝对Galois群之间的同构。这一结果使我们能够减少对混合的完全离散赋值域的伽罗瓦表示的研究。等同)特征与等同的特征(分别混合的)有特点的。

Let p be a rational prime number. In this project, I studied various congruence relations between p-adic Galois representations of complete discrete valuation fields. P-adic Galois representations are important objects for number theory. The aim of this project is to develop methods to reduce study of Galois representations to easier cases by using congruence relations. As the most important achievement in this project, I proved an isomorphism between absolute Galois groups of complete discrete valuation fields of mixed and equal characteristics modulo ramification subgroups. This result enables us to reduce study of Galois representations for complete discrete valuation fields of mixed (resp. equal) characteristic to that for equal (resp. mixed) characteristic.