Title: MATH 662 P-adic L-functions and Iwasawa Theory
Prerequisites: Some background in algebra (Math 654) and algebraic number theory (Math 627) would be useful, but not strictly necessary.
Course Description: The main goals of the course are to construc p-adic interpolations of classical L-functions and to investigate their applications to various
number theoretic phenomena, particularly to class groups and unit groups of cyclotomic fields. This culminates in Iwasawa's formula for the growth of class numbers
in Z_p-towers and the main conjecture of Iwasawa theory. Time permitting, topics will include:
p-adic fields
p-adic analytic functions
Kubota-Leopoldt p-adic L-function
Stickelberger's theorem
Cyclotomic units and Vandiver's conjecture
p-adic measures and distributions
Iwasawa p-adic L-function
Iwasawa's theorem on class groups
Main conjecture of Iwasawa theory
Average time dedicated per week (estimate): I will periodically assign optional homework problems. Depending on the size of the class, I will have students give
presentations on special topics at the end of the semester, so this might entail a little work (researching the topic, preparing the presentation, etc.).