# THE REDUCTION OF CERTAIN TWO DIMENSIONAL SEMISTABLE REPRESENTATIONS

Let p be a prime number and F be a finite extension of Q_{p}. We established an algorithm to compute the semisimplification of the reduction of some irreducible two dimensional crystalline representations with two parameter {h,a_{p}} when v_{p}(a_{p}) is large enough. We improve the known results when p|h. We also extend the algorithm to the two dimensional semistable and non-crystalline representation. We compute the semi-simplification of the reduction when v_{p}(L) large enough and p=2. These results solve the difficulties with the case p=2. The strategies are based on the study of the Kisin modules over O_{F} and Breuil modules over S_{F}. By the theory of Breuil and Theorem of Colmez-Fontaine, these modules are closely related to semistable representations.

## History

## Degree Type

- Doctor of Philosophy

## Department

- Mathematics

## Campus location

- West Lafayette