Mathematics

 Research

1.  Topic on Hilbert-Blumenthal-Carlitz Module

This is my master's thesis at NTHU, supervised by Prof. Fu-Tsun Wei. 

Abstract: In the thesis, we construct the simplest example of Hilbert-Blumenthal $t$-modules in the higher dimensional case by considering the direct sum of Carlitz modules. Also, we study the Galois representation associated with the Hilbert-Blumenthal t-modules in our case via the explicit class field theory developed by Hayes.

Study Notes

1. Frey Curve

This is a project in the course Algebraic Curves (Prof. Ching-Jui Lai) in my junior at NCKU.

2. Kronecker-Weber Theorem

This is a cooperative project in the course Group Scheme and Global Fields (Prof. Jing Yu) in my first-grade graduate school at NTHU.

3. Algebraic Number Theory

This is a study note about algebraic number theory reference by Serge Lang's Algebraic Number Theory.

4. Group Cohomology

This is a project in the course Algebraic Topology (Prof. Hsuan-Yi Liao) in my second-grade graduate school at NTHU.

5. Complex Multiplication

This is a project in the course Complex Multiplication (Prof. Jing Yu) in my second-grade graduate school at NTHU.

6. Eisenstein Series and Hecke Operator

This is a project in the course Modular Form (Prof. Fu-Tsun Wei) in my second-year Graduate school at NTHU.

7. Hayes: Explicit class field theory over rational function fields

This is a study note about Hayes' paper after I studied the Carlitz module.

8. Anderson, Brownawell, Papanikolas: Determination of the algebraic relations among special Γ-values in positive characteristic 

This is a study note for my report on the students' seminar organized by Prof. Chia-Fu Yu.