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THE REDUCTION OF CERTAIN TWO DIMENSIONAL SEMISTABLE REPRESENTATIONS

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posted on 2023-08-07, 15:22 authored by Yifu WangYifu Wang

Let p be a prime number and F be a finite extension of Qp. We established an algorithm to compute the semisimplification of the reduction of some irreducible two dimensional crystalline representations with two parameter {h,ap} when vp(ap) 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 vp(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 OF and Breuil modules over SF. 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

Advisor/Supervisor/Committee Chair

Tong Liu

Additional Committee Member 2

Freydoon Shahidi

Additional Committee Member 3

Baiying Liu

Additional Committee Member 4

Daniel Tuan-Dan Le

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