Math 254B (Number Theory)

This was the official course web page for Math 254B (Number Theory) at UC Berkeley, which I taught during the Spring 2002 semester. The course web page for Math 254A, which I taught in Fall 2001, is here. Math 254B took a detailed look at class field theory, the theory of abelian extensions of number fields, which extends the reciprocity laws of Gauss, Legendre, Hilbert et al.

Note added 9 Nov 2003: I am planning to leave these pages "as is" for now except for updating broken links and posting errata to the course notes in case anyone points them out. (These were largely corrected verbally in the lectures but I didn't put the changes into the notes.) In particular, the contact information for me is incorrect; see my home page for updated information.

Note added 19 Feb 2015: I have compiled a corrected version of the lecture notes, which I strongly recommend in lieu of the originals.

Note added 25 Mar 2020: the final papers have been removed by request.

Stuff to download

Note added 19 Jul 2002: all PostScript files are now compressed using gzip to save space. To decompress, type "gunzip"; your browser or PostScript viewer may do the decompression automatically.

Contact Info

Kiran Kedlaya
757 Evans Hall
email: kedlaya(at)

Homework Policy

The homework policy this term will be somewhat liberal, as this course is considered an "advanced" graduate course. If you are taking the course for a grade, I will expect you to turn in homeworks (approximately weekly) and a final paper. If you are taking the course pass/fail, I will expect you either to turn in the weekly homeworks or to write a final paper; see me for details.


Required: one semester of algebraic number theory (Math 254A or equivalent). More specifically, this includes basic properties of number fields (class group, units group, ramification) and of local fields (p-adic numbers, completions, Hensel's lemma, ramification). Possibly helpful: graduate algebra (Math 250 or equivalent). Also possibly helpful: some familiarity with classical number theory. If you have concerns, see me.

Recommended links

The Berkeley Number Theory Seminar meets Wednesdays from 3:10 to 4:00 PM in 891 Evans, and sometimes on Friday at the same time and place. Prospective students in number theory are encouraged to attend.

If you're shopping for an advisor in number theory, check out the Web pages of Robert Coleman, Hendrik Lenstra, Arthur Ogus, Bjorn Poonen, Ken Ribet, and Paul Vojta.

Some more possibly useful links:

Kiran S. Kedlaya (kedlaya(at)