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 blah.ps.gz"; your browser
or PostScript viewer may do the decompression automatically.
Contact Info
Kiran Kedlaya
757 Evans Hall
email: kedlaya(at)math.berkeley.edu
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.
Prerequisites
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:
- J.S. Milne has
printable notes from a variety of courses, including Algebraic Number Theory (and the class field theory notes mentioned above).
- The Number Theory
Web is the home of all things number-theoretic on the Web.
Kiran S. Kedlaya (kedlaya(at)math.berkeley.edu)