Reading Seminar on Class Field Theory and Related Topics

Spring 2016

Supervisor: Kai-Wen Lan

Schedule

(In each day listed, there were about two hours of lectures.)

• Jan 25, Marshall Smith: Dedekind domains
• Jan 27, Marshall Smith: Different and discriminant
• Feb 1, Marshall Smith: Ramification indices
• Feb 1, Yao Rui Yeo: Decomposition groups and totally ramified extensions
• Feb 3, Yao Rui Yeo: Unramified and tamely ramified extensions
• Feb 8, Yao Rui Yeo: Ramification groups
• Feb 8, Andrew Senger: Generalities of valuations
• Feb 10, Andrew Senger: Valuations and global fields
• Feb 15, Andrew Senger: Adeles and approximations
• Feb 17, Andrew Senger: Units and norm maps
• Feb 17, Marshall Smith: Cyclotomic fields and Kummer extensions
• Feb 22, Yao Rui Yeo: Generalities of group cohomology
• Feb 24, Yao Rui Yeo: Tate cohomology and cup products
• Feb 29, Yao Rui Yeo: Cohomological triviality and Tate's theorem
• Mar 2, Andrew Senger: Cohomology of profinite groups and applications to Galois cohomology
• Mar 7, Marshall Smith: Brauer group of a local field, I
• Mar 9, Marshall Smith: Brauer group of a local field, II
• Mar 21, Yao Rui Yeo: Abelian extensions of local fields, I
• Mar 23, Yao Rui Yeo: Abelian extensions of local fields, II
• Mar 23, Andrew Senger: Formal multiplication in local fields, I
• Mar 30, Andrew Senger: Formal multiplication in local fields, II
• Apr 4, Andrew Senger: Formal multiplication in local fields, III
• Apr 4, Marshall Smith: Ramification groups and conductors, I
• Apr 6, Yao Rui Yeo: Statement of the reciprocity law, I
• Apr 11, Marshall Smith: Ramification groups and conductors, II
• Apr 11, Yao Rui Yeo: Statement of the reciprocity law, II
• Apr 13, Yao Rui Yeo: Statement of the reciprocity law, III
• Apr 13, Andrew Senger: Proof of the reciprocity law, I
• Apr 18, Andrew Senger: Proof of the reciprocity law, II
• Apr 20, Andrew Senger: Proof of the reciprocity law, III