Math 720 schedule
Tuesday Thursday
Aug. 28

In Lecture:
  • Overview of the course
  • Beginning of classical Iwasawa theory

Associated Reading:
  • Chapters 1 - 5 of Washington's book

Video of class (downloadable) 		Aug. 30

In Lecture:
  • Class field theory
  • Classical Iwasawa theory, continued

Associated Reading:
  • Appendix 3 of Washington's book
  • Chapters 1 - 5 of Washington's book

Video of class (downloadable)
Sept. 4

In Lecture:
  • Leopoldt's conjecture and its relation to Z_p extensions of number fields
  • The conjectures of Iwasawa and Greenberg on the psuedonullity of certain Galois groups.

Associated Reading:
  • Chapters 13 of Washington's book

Video of class (downloadable) 		Sept. 6

In Lecture:
  • Structure theory for Z_p[[Z_p]] modules
  • Vandiver's conjecture

Associated Reading:
  • Chapters 13 and 15 of Washington's book

Video of class (downloadable)
Sept. 11

In Lecture:
  • Statement of the classical main conjecture
  • The Herbrand-Ribet Theorem

Associated Reading:
  • Chapters 13 of Washington's book

Video of class (downloadable) 		Sept. 13

In Lecture:
  • The Herbrand-Ribet Theorem, continued
  • Iwasawa modules with no finite submodules

Associated Reading:
  • Chapters 8, 13 and 15 of Washington's book

Video of class (downloadable)
Sept. 18

In Lecture:
  • Iwasawa modules with no finite submodules (continued)
  • Stickleberger's theorem

Associated Reading:
  • Chapters 13 of Washington's book

Video of class (downloadable) 		Sept. 20

In Lecture:
  • Arithmetic topology
  • Gauss sums
  • Stickleberger's Theorem, continued

Associated Reading:
  • Chapters 8, 13 and 15 of Washington's book

Video of class (downloadable)
Sept. 25

In Lecture:
  • p-adic representations of groups
  • Continuous group cohomology
  • Hochschild-Serre Spectral sequence

Associated Reading:
  • The relevant parts of Rubin's "Euler systems"

Video of class (downloadable) 		Sept. 27

In Lecture:
  • Low degree exact sequences arising from spectral sequences
  • Cohomology of modules for cyclic and pro-cyclic groups

Associated Reading:
  • The relevant parts of Rubin's "Euler systems"

Video of class (downloadable)
Oct. 2

In Lecture:
  • pro-finite cohomology of modules for the profinite completion of Z.

Associated Reading:
  • The relevant parts of Rubin's "Euler systems"

Video of class (downloadable) 		Oct. 4

No class - Fall Break.
Oct. 9

In Lecture:
  • Selmer groups

Associated Reading:
  • The relevant parts of Rubin's "Euler systems"

Video of class (downloadable) 		Oct. 11

In Lecture:
  • local and global duaiity
  • Euler systems

Associated Reading:
  • The relevant parts of Rubin's "Euler systems"

Video of class (downloadable) - to be posted
Oct. 9

In Lecture:
  • Selmer groups

Associated Reading:
  • The relevant parts of Rubin's "Euler systems"

Video of class (downloadable) 		Oct. 11

In Lecture:
  • local and global duaiity

Associated Reading:
  • The relevant parts of Rubin's "Euler systems"

Video of class (downloadable)
Oct. 16

In Lecture:
  • global duality, continued
  • Euler systems

Associated Reading:
  • The relevant parts of Rubin's "Euler systems"

Video of class (downloadable) - to be posted 		Oct. 18

In Lecture:
  • Euler systems, continued

Associated Reading:
  • The relevant parts of Rubin's "Euler systems"

Video of class (downloadable)
Oct. 23

In Lecture:
  • The cyclotomic Euler system

Associated Reading:
  • The relevant parts of Rubin's "Euler systems"

Video of class (downloadable) 		Oct. 25

In Lecture:
  • Kolyvagin derivatives

Associated Reading:
  • The relevant parts of Rubin's "Euler systems"

Video of class (downloadable)
Oct. 30

In Lecture:
  • Kolyvagin derivatives, continued

Associated Reading:
  • The relevant parts of Rubin's "Euler systems"

Video of class (downloadable) 		Nov. 1

In Lecture:
  • Local properties of Kolyvagin derivatives at primes not dividing the level

Associated Reading:
  • The relevant parts of Rubin's "Euler systems"

Video of class (downloadable)
Nov. 6

In Lecture:
  • Local properties of Kolyvagin derivatives at primes dividing the level

Associated Reading:
  • The relevant parts of Rubin's "Euler systems"

Video of class (downloadable) 		Nov. 8

In Lecture:
  • Statement of bounds on Selmer groups, classical applications

Associated Reading:
  • The relevant parts of Rubin's "Euler systems"

Video of class (downloadable)
Nov. 13

In Lecture:
  • Sketch of the proof of bounds on Selmer groups in terms of Selmer groups

Associated Reading:
  • The relevant parts of Rubin's "Euler systems"

Video of class (downloadable) 		Nov. 15

In Lecture:
  • Bounding Selmer groups, continued

Associated Reading:
  • The relevant parts of Rubin's "Euler systems"

Video of class (downloadable)
Nov. 20

In Lecture:
  • End of Euler systems

Associated Reading:
  • The relevant parts of Rubin's "Euler systems"

Video of class (downloadable) 		Nov. 22

No class - Thanksgiving Break!
Nov. 27

In Lecture:
  • Ribet's proof of the converse of the Herbrand criterion

Associated Reading:
Video of class (downloadable) 		Nov. 29

In Lecture:
  • Ribet's proof, continued

Associated Reading:
Video of class (downloadable) - to be posted
Dec. 4

In Lecture:
  • Ribet's proof, continued

Associated Reading:
Video of class (downloadable) 		Dec. 6

In Lecture:
  • Ribet's proof, continued

Associated Reading:
Video of class (downloadable)
Last updated: 11/22/18
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