Program
Introduction to p-adic L-functions and Iwasawa theory | |
Student No.： | 50 |
Time： | Mon/Fri 9:50-11:25, 2017-07-03~2017-07-28 |
Instructor： | Li Ma [Bielefeld University] |
Place： | Conference Room 3, Floor 2, Jin Chun Yuan West Building |
Starting Date： | 2017-7-3 |
Ending Date： | 2017-7-28 |
Description:
p-adic L-functions are p-adic analogues of classical L-functions. As their complex cousins, they play important roles in number theory, representation theory and arithmetic geometry, notably in the p-adic Langlands program.
This course aims at motivating the basic notions, results and conjectures in this domain, clarified with concrete examples. It will consist of two parts, the analytic part and the algebraic part. In the analytic part, one defines p-adic L-functions via interpolation of special values of complex L-functions. In the algebraic part, which is Iwasawa theory, we define Iwasawa algebras and modules, and will see how they are related to p-adic L-functions. We end the course with the main conjecture of Iwasawa and some applications of the theory.
As an introductory course, it will be designed as self-contained as possible.
Prerequisite:
Algebraic number theory, commutative algebra, complex analysis.
Reference:
[1] K. Iwasawa, “On Gamma-extensions of algebraic number fields”, Bulletin of the American Mathematical Society, 65 (4), 1959.
[2] A. Wiles, “The Iwasawa Conjecture for Totally Real Fields”, Annals of Mathematics, 131 (3), 1990.
[3] B. Mazur, A. Wiles, “Class fields of abelian extensions of Q”, Inventiones Mathematicae, 76 (2), 1984.