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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

THE REDUCTION OF CERTAIN TWO DIMENSIONAL SEMISTABLE REPRESENTATIONS

Yifu Wang (16644759) 07 August 2023 (has links)
<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>

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