Algebraic Number Theory, Spring 2009

    Date of the first class: 2009.2.26. No meeting on 2009.2.19.

Course Information

• Office Hours: By appointments.


• Textbooks and References:
• [1] Z.I. Borevich and I.R. Shafarevich, Number theory.
• [2] Daniel A. Marcus, Number fields.
• [3] Yifan Yang's course notes.


• Grading:
  • Homework assignments - 30%
  • Midterm exam - 30%
  • Presentation - 40%


• Ceiba Website: http://ceiba.ntu.edu.tw/972AlgNT

Contents

• 2.26. Number fields (Cf. [2], Ch 2; [3], Ch 1)
• 3.5. Rings of integers ([2], Ch 2; [3], Ch 1)
• 3.12. 江政融 : Some Galois theory ([2], Appendix; [3], Appendix);
        Prime decomposition I ([2], Ch 3; [3], Ch 2)
• 3.19. 林鈺傑 : Algebraic integers of cyclotomic fields ([2], Ch 2; [3], Ch 1);
        Prime decomposition II ([2], Ch 4; [3], Ch 2)
• 3.26. 曾宇揚 : Function field analogs;
        Examples ([2], Ch 4; [3], Ch 2)
• 4.2. Spring break
• 4.9. Decomposition and inertia groups ([2], Ch 4; [3], Ch 2)
• 4.16. 李彥穎 : The different ideal ([2], Ex 3.33 - 39, 4.17);
        The ideal class group ([2], Ch 5)
• 4.23. 林金毅 : Abelian extensions over Q ([2], Ex 4.29 - 38);
        The group of units ([2], Ch 5)
• 4.30. 楊策仲 : Special case of Fermat's last theorem, I ([2], Ch 1);
        Distribution of ideals ([2], Ch 6)
• 5.7. 江謝良州 : Special case of Fermat's last theorem, II ([1], § 5.7);
        The Dedekind zeta function ([2], Ch 7)
• 5.14. 殷灝 : Characters ([1], § A.5);
        The class number formula ([2], Ch 7)
• 5.21. Conference: Modular Forms and Function Field Arithmetic
• 5.28. Holiday
• 6.4. 蘇邦彥 : p-adic fields ([1], Ch 1);
       L-functins of characters ([2], Ch 7)
• 6.11. 陳星谷 : Bernoulli numbers ([1], § 5.8);
        Miscellanea ([1], Ch 5)

Assignments

    #1, #2, #3

Links

    Online Lecture Notes on Algebraic Number Theory

    Online Textbooks in Mathematics: Stefanov

    Number Theory Web

Last updated on 2009.5.31.