Monday 
Wednesday 
Friday 
Sept. 13
In Lecture (room 4C4, 3  4 p.m.):
 Motivation: Higher dimensional class field theory
 Definition of Grothendieck groups and K_0(R)
Associated Reading (from gigapedia)
 Rosenberg, "Algebraic Ktheory and its applications," Chapter 1.
Video of class (streaming)
Video of class (downloadable)
 Sept. 15
In Lecture (room 4C6, 2:30  3 p.m.):
 Module theoretic approaches to K_0(R)
Associated Reading:
 Serre, Linear representations of finite groups.
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Video of class (downloadable)
 Sept. 17
In Lecture (room 4C6, 1  2 p.m.):
 Cristian Pop will give a lecture in class.

Sept. 20
In Lecture (room 4C4, 3  4 p.m.):
 K_0(R) via infinite matrices: functorial properties and examples
Associated Reading
links.
 Rosenberg, "Algebraic Ktheory and its applications," Chapter 1.
Video of class (streaming)  not available
Video of class (downloadable)  not available
 Sept. 22
In Lecture (room 4C6,10  11 a.m..):
Associated Reading:
 Rosenberg, "Algebraic Ktheory and its applications," Chapter 1.
Video of class (streaming)
Video of class (downloadable)
 Sept. 24
In Lecture (room 4C6, 1  2 p.m.):
 Mayer Vietoris construction of projective modules
Associated Reading:
Video of class (streaming)
Video of class (downloadable)

Sept. 27
In Lecture (room 4C4, 3  4 p.m.):
 Mayer Vietoris construction, continued
 Vector bundles and topological Ktheory
Associated Reading
 Rosenberg, "Algebraic Ktheory and its applications," Chapter 1.
Video of class (streaming)
Video of class (downloadable)
 Sept. 29
In Lecture (room 4C6,10  11 a.m..):
 Overview of Stieffel Whitney classes and Chern classes
 Start of the proof of Swan's theorem
Associated Reading:
 Rosenberg, "Algebraic Ktheory and its applications," Chapter 1.
Video of class (streaming)
Video of class (downloadable)
 Oct. 1
In Lecture (room 4C6, 1  2 p.m.):
 Completion of the proof of Swan's theorem
Associated Reading:
Video of class (streaming)
Video of class (downloadable)

Oct. 4
In Lecture (room 4C4, 3  4 p.m.):
 Vector bundles and patching
 Continuous Cech cohomology
Associated Reading
links.
 Rosenberg, "Algebraic Ktheory and its applications," Chapter 1.
 J. Milnor and J. Stasheff, "Characteristic Classes."
 C. Weibel's "KBook", chapter 1
Video of class (streaming)
Video of class (downloadable)
 Oct. 6
In Lecture (room 4C6,10  11 a.m..):
 Stieffel Whitney Classes and Chern Classes
Associated Reading:
 Rosenberg, "Algebraic Ktheory and its applications," Chapter 1.
 J. Milnor and J. Stasheff, "Characteristic Classes."
 C. Weibel's "KBook", chapter 1
 Lang's algebra on the Clifford Algebras and the Pin group.
Video of class (streaming)
Video of class (downloadable)
 Oct. 8
In Lecture (room 4C6, 1  2 p.m.):
 Stieffel Whitney Classes and Chern Classes, continued
 The Pin group
Associated Reading:
 Rosenberg, "Algebraic Ktheory and its applications," Chapter 1.
 J. Milnor and J. Stasheff, "Characteristic Classes."
 C. Weibel's "KBook", chapter 1
 Lang's algebra on the Clifford Algebras and the Pin group.
Video of class (streaming)
Video of class (downloadable)

Oct. 11
No class: Fall Break!
 Oct. 13
In Lecture (room 4C6,10  11 a.m..):
 The Whitehead group K_1(\Lambda)
Associated Reading:
Video of class (streaming)
Video of class (downloadable)
 Oct. 15
No class: postponed.

Oct. 18
In Lecture (room 4C6,10  11 a.m..):
 The Whitehead group K_1(\Lambda), continued
 Long exact sequences
Associated Reading:
Video of class (streaming)
Video of class (downloadable)
 Oct. 20
In Lecture (room 4C4, 12 noon  1 p.m, note time change):
 K_2(\Lambda) and the Steinberg group
Associated Reading:
 Rosenberg, "Algebraic Ktheory and its applications," Chapter 4.
 Milnor, "Algebraic Ktheory," Chapter 5.
Video of class (streaming)
Video of class (downloadable)
 Oct. 22
No class: postponed.

Oct. 25
In Lecture (room 4C6,10  11 a.m..):
 Ktheory and the leading terms in the expansions of Lseries at integers
Associated Reading:

 Be?linson's conjectures on special values of $L$Lfunctions, 273Ð304, Perspect. Math., 4, Academic Press, Boston, MA, 1988.
Video of class (streaming)
Video of class (downloadable)
 Oct. 27
In Lecture
Associated Reading:
 Kneser, M. Semisimple algebraic groups. 1967 Algebraic Number. Theory (Proc. Instructional Conf., Brighton, 1965) pp. 250Ð265.
Video of class (streaming)
Video of class (downloadable)
 Oct. 29
In Lecture
 The Steinberg group and K_2, continued
Associated Reading:
 Rosenberg, "Algebraic Ktheory and its applications," Chapter 4.
 Milnor, "Algebraic Ktheory," Chapter 5.
Video of class (streaming)  to be posted
Video of class (downloadable)  to be posted

Nov. 1
In Lecture (room 4C6,10  11 a.m..):
 Universal central extensions and the Steinberg group
Associated Reading:
 Rosenberg, "Algebraic Ktheory and its applications," Chapter 4.
 Milnor, "Algebraic Ktheory," Chapter 5.
Video of class (streaming)
Video of class (downloadable)
 Nov. 3
In Lecture
 Long exact sequences in Ktheory
 K_2 and symbols
Associated Reading:
 Milnor, "Algebraic Ktheory," Chapters 6, 11.
 Rosenberg, "Algebraic Ktheory and its applications," Chapter 4.
Video of class (streaming)
Video of class (downloadable)
 Nov. 5
In Lecture
 K_2 and symbols (continued)
Associated Reading:
 Rosenberg, "Algebraic Ktheory and its applications," Chapter 4.
 Milnor, "Algebraic Ktheory," Chapter 5.
Video of class (streaming)
Video of class (downloadable) 

Nov. 8
In Lecture (room 4C6,10  11 a.m..):
 Quillen's + construction
 Quillen's Q construction
Associated Reading:
 Rosenberg, "Algebraic Ktheory and its applications," Chapter 5.
Video of class (streaming)
Video of class (downloadable)
 Nov. 10
In Lecture
 Quillen's Q construction, continued
Associated Reading:
 Rosenberg, "Algebraic Ktheory and its applications," Chapter 5.
Video of class (streaming)
Video of class (downloadable)
 Nov. 12
In Lecture
 End of discussion of the Qconstruction
Associated Reading:
 Rosenberg, "Algebraic Ktheory and its applications," Chapter 5.
Video of class (streaming)
Video of class (downloadable) 

Nov. 15
In Lecture (room 4C6,10  11 a.m..):
 Overview of some papers on classfield theory to be discussed
 Recap of Classfield theory for local fields via the Brauer group
Associated Reading:
 J. P. Serre, Corps Locaux
Video of class (streaming)
Video of class (downloadable)
 Nov. 17
In Lecture
 Recap of classfield theory for local fields: the Artin map
 Start of classfield theory of curves over local fields
Associated Reading:
 J. P. Serre, Corps Locaux
 Algebraic KTheory and Classfield Theory for Arithmetic Surfaces, by Spencer Bloch Source: The Annals of Mathematics, Second Series, Vol. 114, No. 2 (Sep., 1981), pp. 229265
 Class field theory for curves over local fields, by S. Saito, J. Number Theory 21 (1985), no. 1, 44Ð80.
Video of class (streaming)
Video of class (downloadable)
 Nov. 19
In Lecture
 Classfield theory on Curves
Associated Reading:
 Algebraic KTheory and Classfield Theory for Arithmetic Surfaces, by Spencer Bloch Source: The Annals of Mathematics, Second Series, Vol. 114, No. 2 (Sep., 1981), pp. 229265
 Class field theory for curves over local fields, by S. Saito, J. Number Theory 21 (1985), no. 1, 44Ð80.
Video of class (streaming)
Video of class (downloadable) 

Nov. 22
In Lecture
 Classfield theory on Curves (continued)
Associated Reading:
 Algebraic KTheory and Classfield Theory for Arithmetic Surfaces, by Spencer Bloch Source: The Annals of Mathematics, Second Series, Vol. 114, No. 2 (Sep., 1981), pp. 229265
 Class field theory for curves over local fields, by S. Saito, J. Number Theory 21 (1985), no. 1, 44Ð80.
Video of class (streaming)
Video of class (downloadable)
 Nov. 24
In Lecture
 Classfield theory on Curves
Associated Reading:
 Algebraic KTheory and Classfield Theory for Arithmetic Surfaces, by Spencer Bloch Source: The Annals of Mathematics, Second Series, Vol. 114, No. 2 (Sep., 1981), pp. 229265
 Class field theory for curves over local fields, by S. Saito, J. Number Theory 21 (1985), no. 1, 44Ð80.
Video of class (streaming)
Video of class (downloadable)
 Nov. 26
In Lecture
 No Class  Thanksgiving Break!

Nov. 29
In Lecture
 Classfield theory on Curves (continued)
 Tate curves
Associated Reading:
 Class field theory for curves over local fields, by S. Saito, J. Number Theory 21 (1985), no. 1, 44Ð80.
 The arithmetic of elliptic curves, J. Silverman
 Elliptic functions, S. Lang
Video of class (streaming))
Video of class (downloadable)
 Dec. 1
In Lecture
 Tate curves, continued
 Classfield theory for two dimensional local fields
Associated Reading:
 Class field theory for curves over local fields, by S. Saito, J. Number Theory 21 (1985), no. 1, 44Ð80.
 The arithmetic of elliptic curves, J. Silverman
 Elliptic functions, S. Lang
Video of class (streaming)
Video of class (downloadable)
 Dec. 3
In Lecture
 Classfield theory for two dimensional local fields (continued)
Associated Reading:
 Class field theory for curves over local fields, by S. Saito, J. Number Theory 21 (1985), no. 1, 44Ð80.
Video of class (streaming)
Video of class (downloadable)

Dec. 6
In Lecture
 Classfield theory for two dimensional local fields (continued)
Associated Reading:
 Class field theory for curves over local fields, by S. Saito, J. Number Theory 21 (1985), no. 1, 44Ð80.
Video of class (streaming))
Video of class (downloadable)
 Dec. 8
In Lecture
 Classfield theory for two dimensional complete local rings
Associated Reading:
 Class field theory for curves over local fields, by S. Saito, J. Number Theory 21 (1985), no. 1, 44Ð80.
 Invitation to Higher Local Fields, I. Fesenko (see gigapedia).
Video of class (streaming)
Video of class (downloadable)
 Dec. 10
In Lecture
 Classfield theory for two dimensional complete local rings (continued)
Associated Reading:
 Class field theory for curves over local fields, by S. Saito, J. Number Theory 21 (1985), no. 1, 44Ð80.
 Invitation to Higher Local Fields, I. Fesenko (see gigapedia).
Video of class (streaming)
Video of class (downloadable)
