Besides my research project, I was able to sit in on the graduate courses Advanced Topics in Algebra E & F, taught by Prof. Tadashi Ochiai at Institute of Science Tokyo. Dr. Soma (my supervisor) suggested I join these lectures, so I could get some exposure to advanced algebra alongside my research on modular forms. Grateful to Prof. Tadashi Ochiai for allowing me to sit in on his lectures.
The goal of the course was to understand Iwasawa theory: the Iwasawa main conjecture, which relates ideal class groups along the cyclotomic tower to p-adic L-functions. It starts from ramification in number fields, goes through p-adic fields, zeta and L-functions, Zp-extensions and the Iwasawa algebra, and ends with p-adic Hodge theory, Selmer groups and elliptic curves.
I did not understand most of the material during the lectures. Many statements in class were only stated (“it is well known that…”) and many proofs were skipped, so most of the proofs in these notes were written afterwards, and with the help of Claude Code (Opus 5.5 High-Ultracode).
Again, shout-out to Orlando Ferrari’s lecture notes project, which inspired the way I wrote up these notes.
I don't claim my notes were perfect; please read and double-check the words; any mistakes are mine. If you spot one, feel free to reach out to me on GitHub.