The Reduction of Certain Two Dimensional Semistable Representations

Yifu Wang, Purdue University

Abstract

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 that [1] can not deal 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.

Degree

Ph.D.

Advisors

Liu, Purdue University.

Subject Area

Mathematics

COinS