<p>Let p be a prime number and F be a finite extension of Q<sub>p</sub>. We established an algorithm to compute the semisimplification of the reduction of some irreducible two dimensional crystalline representations with two parameter {h,a<sub>p</sub>} when v<sub>p</sub>(a<sub>p</sub>) 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<sub>p</sub>(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<sub>F</sub> and Breuil modules over S<sub>F</sub>. By the theory of Breuil and Theorem of Colmez-Fontaine, these modules are closely related to semistable representations.</p>
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/23741631 |
| Date | 07 August 2023 |
| Creators | Yifu Wang (16644759) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/THE_REDUCTION_OF_CERTAIN_TWO_DIMENSIONAL_SEMISTABLE_REPRESENTATIONS/23741631 |
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