Notes will be posted here in the afternoons following the lecture.
Lecture Notes |
Date |
Topic |
|
|---|---|---|---|
| #1 | | Wednesday, | Sept. 3, Outline of the course, sums of squares | |
| #2 | | Friday, | Sept. 5, Algebraic integers | |
| #3 | | Monday, | Sept. 8, Trace, norm, discriminant | |
| #4 | | Wednesday, | Sept. 10, integral bases | |
| #5 | | Friday, | Sept. 12, ideal factorization, Dedekind domains I | |
| #6 | | Monday, | Sept. 15, ideal factorization, Dedekind domains II | |
| #7 | | Wednesday, | Sept. 17, fractional ideals, class group, lattices | |
| #8 | | Friday, | Sept. 19, Minkowski's theory of lattices | |
| #9 | | Monday, | Sept. 22, Finiteness of class group, start of discussion on units | |
| #10 | | Wednesday, | Sept. 24, End of Dirichlet unit theorem, regulator | |
| #11 | | Friday, | Sept. 26, Factoring primes in Dedekind domains | |
| #12 | | Monday, | Sept. 29, Factoring primes in Dedekind domains II | |
| #13 | | Wednesday, | Oct. 1, Factoring primes in Galois extensions | |
| #14 | | Friday, | Oct. 3, Using SAGE to do computational algebraic number theory | |
| #15 | | Monday, | Oct. 6, Cyclotomic fields I | |
| #16 | | Wednesday, | Oct. 8, Cyclotomic fields II | |
| #17 | | Friday, | Oct. 10, Localization | |
| #18 | | Monday, | Oct. 13, Units and class groups in localizations | |
| #19 | | Wednesday, | Oct. 15, one dimensional Noetherian domains | |
| #20 | | Friday, | Oct. 17, Geometric intuition | |
| #21 | | Monday, | Oct. 20, Affine schemes for 1-dimensional domains | |
| #22 | | Wednesday, | Oct. 22, Function fields | |
| #23 | | Friday, | Oct. 24, Introduction to valuation theory | |
| #24 | | Monday, | Oct. 27, completeness of p-adic numbers | |
| #25 | | Wednesday, | Oct. 29, classification of valuations | |
| #26 | | Friday, | Oct. 31, completions of number fields | |
| #27 | | Monday, | Nov. 3, non-archimedean valuations, Hensel's lemma | |
| #28 | | Wednesday, | Nov. 5, Extensions of absolute values | |
| #29 | | Friday, | Nov. 7, Intro to local fields | |
| #30 | | Monday, | Nov. 10, Unit theorems | |
| #31 | | Wednesday, | Nov. 12, Logarithm in p-adic fields | |
| #32 | | Friday, | Nov. 14, Extensions of Henselian fields | |
| #33 | | Monday, | Nov. 17, The structure of unramified extensions | |
| #34 | | Wednesday, | Nov. 19, Extension of valuations in number fields | |
| #35 | | Friday, | Nov. 21, The fundamental identity of local extensions | |
| #36 | | Monday, | Nov. 24, Galois theory of local extensions | |
| #37 | | Monday, | Dec. 1, Formalism of profinite groups | |
| #38 | | Wednesday, | Dec. 3, Formalism of valuations | |
| #39 | | Friday, | Dec. 5, The reciprocity map | |
| #40 | | Monday, | Dec. 8, local class field theory and Kronecker-Weber theorems | |
| #41 | | Wednesday, | Dec. 10, global class field theory | |
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