Math 204A videos

Topics by date (with videos, references, notes, and boards):

• Oct 2 (F): Overview of the course (video, boards, Miro live). Notes: algebraic numbers and algebraic integers.
  
• Oct 5 (M): Gaussian and Eisenstein integers (video, boards, Miro live). References: Neukirch I.1, Jarvis chapter 1, brilliant.org.
  
• Oct 7 (W): Eisenstein and other quadratic integers (video, boards, Miro live).
  
• Oct 9 (F): Rings of integers in number fields (boards, Miro live). References: Neukirch I.2; Milne chapter 2 (for symmetric polynomials), brilliant.org.
  This lecture was not fully recorded due to a technical issue. The first video below is missing about 15 minutes; the second video is a supplement to replace the missing segment.
  
  
• Oct 12 (M): Unique factorization of ideals (video, boards, Miro live). References: Neukirch I.2, I.3.
  
• Oct 14 (W): Discriminant of a basis, proof of unique factorization, fractional ideals (video/, video, boards, Miro live). References: Neukirch I.2, I.3.
  
• Oct 16 (F): The lattice of a number field (video, boards, Miro live). References: Neukirch I.5.
  
• Oct 19 (M): Minkowski's theorem (video, boards, Miro live). References: Neukirch I.4, I.5, I.6.
  
• Oct 21 (W): The class number; the multiplicative lattice of a number field (video, boards, Miro live). References: Neukirch I.5, I.6, I.7.
  
• Oct 23 (F): The multiplicative lattice and the units theorem (video, boards, Miro live). References: Neukirch I.6, I.7.
  
• Oct 26 (M): Computational tools for algebraic number theory (video, boards, Miro live).
  
• Oct 28 (W): Extensions of Dedekind domains (video, boards, Miro live). References: Neukirch I.8.
  
• Oct 30 (F): continuation (video/, boards, Miro live).
  
• Nov 2 (M): Cyclotomic fields (video, boards, Miro live). References: Neukirch I.10, Marcus chapter 2.
  
• Nov 4 (W): Galois groups, ramification, and splitting (video, boards, Miro live). References: Neukirch I.9.
  
• Nov 6 (F): continuation (video, boards, Miro live).
  
• Nov 9 (M): Localization (video, boards, Miro live). References: Neukirch I.11.
  
• No lecture on Wednesday, November 11.
• Nov 13 (F): continuation (video, boards, Miro live).
  
• Nov 16 (M): Different and discriminant (video, boards, Miro live). References: Neukirch III.2.
  
• Nov 18 (W): continuation (video, boards, Miro live).
  
• Nov 20 (F): Structure of ramification groups (video, boards, Miro live). References: Neukirch II.10.
  
• Nov 23 (M): p-adic numbers (video, boards, Miro live). References: Neukirch II.1.
  
• Nov 25 (W): p-adic absolute value (video, boards, Miro live). References: Neukirch II.2, II.4.
  
• No lecture on Friday, November 27.
• Nov 30 (M): Valuations (video, boards, Miro live). References: Neukirch II.3.
  
• Dec 2 (W): Extensions of valuations (video, boards, Miro live). References: Neukirch II.4. Notes: extension of valuations.
  
• Dec 4 (F): Hensel's lemma (video, boards, Miro live). References: Neukirch II.4.
  
• Dec 7 (M): Newton polygons (video, boards, Miro live). References: Neukirch II.6.
  
• Dec 9 (W): The Kronecker-Weber theorem: preview of Math 204B (video, boards, Miro live). References: notes on class field theory, chapter 1.
  
• Dec 11 (F): The local Kronecker-Weber theorem (video, boards, Miro live). References: notes on class field theory, chapter 1.