Math 204B videos

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

Jan 4 (M): Kummer theory and the Kronecker-Weber theorem (video, boards, Miro live). References: CFT notes 1.1, 1.2, 1.3. See also "From quadratic reciprocity to class field theory" (pdf).
Jan 6 (W): The Hilbert class field (video, boards, Miro live). References: CFT notes 2.1.
Jan 8 (F): Generalized ideal class groups and the Artin reciprocity law (video, boards, Miro live). References: CFT notes 2.2 .

Jan 11 (M): The principal ideal theorem (video, boards, Miro live). References: CFT notes 2.3.
Jan 13 (W): Zeta functions and the Chebotarev density theorem (video, boards, Miro live). References: CFT notes 2.4.
~~Jan 15 (F)~~: Cohomology of finite groups, I (video, boards, Miro live). References: CFT notes 3.1. Note: this lecture is rescheduled to Thursday, January 14 at 4pm.
Jan 20 (W): Cohomology of finite groups, II (video, boards Miro live). References: CFT notes 3.2.
Jan 22 (F): Extended functoriality; homology and Tate groups (video, boards, Miro live). References: CFT notes 3.2, 3.3.
Jan 25 (M): Herbrand quotient; profinite groups (video, boards, Miro live). References: CFT notes 3.4, 3.5.
Jan 27 (W): cohomology of profinite groups; overview of local class field theory (video, boards, Miro live). References: CFT notes 3.5, 4.1.
Jan 29 (F): overview of local class field theory (video, boards, (Miro live). References: CFT notes 4.1.
Feb 1 (M): cohomology of local fields (a href="https://mediaspace.ucsd.edu/media/Math+204B%2C+Lecture+2021-02-01/1_15sjhcoj">video, boards, Miro live). References: CFT notes 4.2.
Feb 3 (W): cohomology of local fields; Tate's theorem (video, boards, Miro live). References: CFT notes 4.2, 4.3.

Feb 5 (F): local CFT via Tate's theorem (video, boards, Miro live). References: CFT notes 4.3.

Feb 8 (M): abstract CFT (video, boards, Miro live). References: CFT notes 5.1, 5.2.

Feb 10 (W): the abstract reciprocity map and reciprocity law (video, boards, Miro live). References: CFT notes 5.2, 5.3.

Feb 12 (F): the abstract reciprocity law; the filtration on a local Galois group (video, boards, Miro live). References: CFT notes 5.3, 4.4.

Feb 17 (W): adèles (video, boards, Miro live). References: CFT notes 6.1.

Feb 19 (F): idèles and class groups (video, boards, Miro live). References: CFT notes 6.2.

Feb 22 (M): adèles and idèles in field extensions; the theorems of adelic CFT (video, boards, Miro live). References: CFT notes 6.3, 6.4.

Feb 24 (W): local-global compatibility for the reciprocity law; overview of the proofs of global CFT (video, boards, Miro live). References: CFT notes 6.4, 6.5.

Feb 26 (F): the First Inequality (video, boards, Miro live). References: CFT notes 7.1.

Mar 1 (M): the Second Inequality: analytic proof (video, boards, Miro live). References: CFT notes 7.2.

Mar 3 (W): the abstract reciprocity map; reductions for the existence theorem (video, boards, Miro live). References: CFT notes 7.3, 7.4.

Mar 5 (F): the key case of the existence theorem; algebraic proof of the Second Inequality (video, boards, Miro live). References: CFT notes 7.4.

Mar 8 (M): local-global compatibility (video, boards, Miro live). References: CFT notes 7.5.

Mar 10 (W): Brauer groups of number fields (video, boards, Miro live). References: CFT notes 7.6.

Mar 12 (F): preview of Math 204C: adelic Fourier analysis (video, boards, Miro live). References: CFT notes 6.6; see also Cassels-Fröhlich, chapter 15 and Ramakrishnan-Valenza, Fourier Analysis on Number Fields (the Math 204C textbook).