# Course

Playlist: <https://mediaspace.ucsd.edu/playlist/dedicated/1_x0lpso72/1_nm8mfpzj>

-   [ ] Jan 4 (M): Kummer theory and the Kronecker-Weber theorem
 ([https://kskedlaya.org/papers/pcm.pdf)](https://kskedlaya.org/papers/pcm.pdf)).
-   [ ] Jan 6 (W): The Hilbert class field
 ([https://kskedlaya.org/cft/sec_hilbert.html](https://kskedlaya.org/cft/sec_hilbert.html).
-   [ ] Jan 8 (F): Generalized ideal class groups and the Artin reciprocity law
 ([https://kskedlaya.org/cft/sec_artinrec.html](https://kskedlaya.org/cft/sec_artinrec.html).
-   [ ] Jan 11 (M): The principal ideal theorem
 ([https://kskedlaya.org/cft/sec_principal.html](https://kskedlaya.org/cft/sec_principal.html).
-   [ ] Jan 13 (W): Zeta functions and the Chebotarev density theorem
 ([https://kskedlaya.org/cft/sec_zeta.html](https://kskedlaya.org/cft/sec_zeta.html).
-   [ ] Jan 15 (F): Cohomology of finite groups, I
 ([https://kskedlaya.org/cft/sec_cohom1.html](https://kskedlaya.org/cft/sec_cohom1.html). Note: this lecture is rescheduled to Thursday, January 14 at 4pm.
-   [ ] Jan 20 (W): Cohomology of finite groups, II 
	([https://kskedlaya.org/cft/sec_cohom2.html](https://kskedlaya.org/cft/sec_cohom2.html).
-   [ ] Jan 22 (F): Extended functoriality; homology and Tate groups 
([https://kskedlaya.org/cft/sec_homology.html](https://kskedlaya.org/cft/sec_homology.html).
-   [ ] Jan 25 (M): Herbrand quotient; profinite groups 
([https://kskedlaya.org/cft/sec_profinite.html](https://kskedlaya.org/cft/sec_profinite.html).
-   [ ] Jan 27 (W): cohomology of profinite groups; overview of local class field theory
 ([https://kskedlaya.org/cft/sec_localrecip.html](https://kskedlaya.org/cft/sec_localrecip.html).
-   [ ] Jan 29 (F): overview of local class field theory
 ([https://kskedlaya.org/cft/sec_localrecip.html](https://kskedlaya.org/cft/sec_localrecip.html).
-   [ ] Feb 1 (M): cohomology of local fields 
([https://kskedlaya.org/cft/sec_localcomp.html](https://kskedlaya.org/cft/sec_localcomp.html).
-   [ ] Feb 3 (W): cohomology of local fields; Tate's theorem
 ([https://kskedlaya.org/cft/sec_tatethm.html](https://kskedlaya.org/cft/sec_tatethm.html).
-   [ ] Feb 5 (F): local CFT via Tate's theorem
 ([https://kskedlaya.org/cft/sec_tatethm.html](https://kskedlaya.org/cft/sec_tatethm.html).
-   [ ] Feb 8 (M): abstract CFT
 ([https://kskedlaya.org/cft/sec_abstractcft2.html](https://kskedlaya.org/cft/sec_abstractcft2.html).
-   [ ] Feb 10 (W): the abstract reciprocity map and reciprocity law 
([https://kskedlaya.org/cft/sec_abstractcft3.html](https://kskedlaya.org/cft/sec_abstractcft3.html).
-  [ ]  Feb 12 (F): the abstract reciprocity law; the filtration on a local Galois group 
([https://kskedlaya.org/cft/sec_filtration.html](https://kskedlaya.org/cft/sec_filtration.html).
-   [ ] Feb 17 (W): adèles
 ([https://kskedlaya.org/cft/sec_adeles.html](https://kskedlaya.org/cft/sec_adeles.html).
-   [ ] Feb 19 (F): idèles and class groups
 ([https://kskedlaya.org/cft/sec_ideles.html](https://kskedlaya.org/cft/sec_ideles.html).
-   [ ] Feb 22 (M): adèles and idèles in field extensions; the theorems of adelic CFT
 ([https://kskedlaya.org/cft/sec_adelic-recip.html](https://kskedlaya.org/cft/sec_adelic-recip.html).
-   [ ] Feb 24 (W): local-global compatibility for the reciprocity law; overview of the proofs of global CFT 
([https://kskedlaya.org/cft/sec_adelic-overview.html](https://kskedlaya.org/cft/sec_adelic-overview.html).
-   [ ] Feb 26 (F): the First Inequality
 ([https://kskedlaya.org/cft/sec_ideles-cohom1.html](https://kskedlaya.org/cft/sec_ideles-cohom1.html).
-   [ ] Mar 1 (M): the Second Inequality: analytic proof
 ([https://kskedlaya.org/cft/sec_ideles-cohom2.html](https://kskedlaya.org/cft/sec_ideles-cohom2.html).
-   [ ] Mar 3 (W): the abstract reciprocity map; reductions for the existence theorem
 ([https://kskedlaya.org/cft/sec_existence.html](https://kskedlaya.org/cft/sec_existence.html).
-   [ ] Mar 5 (F): the key case of the existence theorem; algebraic proof of the Second Inequality 
([https://kskedlaya.org/cft/sec_existence.html](https://kskedlaya.org/cft/sec_existence.html).
-   [ ] Mar 8 (M): local-global compatibility
 ([https://kskedlaya.org/cft/sec_connection.html](https://kskedlaya.org/cft/sec_connection.html).
-   [ ] Mar 10 (W): Brauer groups of number fields
 ([https://kskedlaya.org/cft/sec_connection.html](https://kskedlaya.org/cft/sec_connection.html).
-   [ ] Mar 12 (F): preview of Math 204C: adelic Fourier analysis
 ([http://dx.doi.org/10.1007/978-1-4757-3085-2/) (the Math 204C textbook](http://dx.doi.org/10.1007/978-1-4757-3085-2/) (the Math 204C textbook).