Congruence relations between p-adic crystalline representations

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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.