UCSB Math Department

Graduate Number Theory Seminar
Winter 2021

Organizers: Mulun Yin.

Meets Wednesdays 1-2 PM PT.


This fall, we will discuss the first few chapters of the book Cohomology of Number Fields by Neukirch, Schmidt and Wingberg. We do not have assigned speakers and the seminar will be in the form of free discussion.


Date Title
Septemper 23 Organizational meeting
October 6 CH I. Section 2. Interpretations of H^0, H^1, H^2 and H^n and Tate cohomology
CH I. Section 4. Cup product
October 13 CH VI. Section 1. Cohomology of Additive Group
CH VI. Section 2. Hilbert's Satz 90
October 20 CH VI. Section 4. The Brauer Group CH VI. Section 5. The Milnor K-Groups CH VI. Section 6. Dimension of Fields
October 27 CH VII. Section 1. Cohomology of the Multiplicative Group
November 3 CH VII. Section 1. Cohomology of the Multiplicative Group (cont'd)
CH VII. Section 2. The Local Duality Theorem
November 10 CH VII. Section 4. Galois Module Structure of the Multiplicative Group
November 17 CH VII. Section 5. Explicit Determination of Local Galois Groups
November 24 (Thanksgiving week)
December 1 (Cancelled)