Math 720 schedule
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 K-theory 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.
Video of class (streaming)
Video of class (downloadable)
| Sept. 17
In Lecture (room 4C6, 1 - 2 p.m.):
- Cristian Pop will give a lecture in class.
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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 K-theory 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 K-theory 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)
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Sept. 27
In Lecture (room 4C4, 3 - 4 p.m.):
- Mayer Vietoris construction, continued
- Vector bundles and topological K-theory
Associated Reading
- Rosenberg, "Algebraic K-theory 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 K-theory 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)
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Oct. 4
In Lecture (room 4C4, 3 - 4 p.m.):
- Vector bundles and patching
- Continuous Cech cohomology
Associated Reading
links.
- Rosenberg, "Algebraic K-theory and its applications," Chapter 1.
- J. Milnor and J. Stasheff, "Characteristic Classes."
- C. Weibel's "K-Book", 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 K-theory and its applications," Chapter 1.
- J. Milnor and J. Stasheff, "Characteristic Classes."
- C. Weibel's "K-Book", 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 K-theory and its applications," Chapter 1.
- J. Milnor and J. Stasheff, "Characteristic Classes."
- C. Weibel's "K-Book", chapter 1
- Lang's algebra on the Clifford Algebras and the Pin group.
Video of class (streaming)
Video of class (downloadable)
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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.
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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 K-theory and its applications," Chapter 4.
- Milnor, "Algebraic K-theory," Chapter 5.
Video of class (streaming)
Video of class (downloadable)
| Oct. 22
No class: postponed.
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Oct. 25
In Lecture (room 4C6,10 - 11 a.m..):
- K-theory and the leading terms in the expansions of L-series at integers
Associated Reading:
-
- Be?linson's conjectures on special values of $L$L-functions, 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. Semi-simple 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 K-theory and its applications," Chapter 4.
- Milnor, "Algebraic K-theory," Chapter 5.
Video of class (streaming) - to be posted
Video of class (downloadable) - to be posted
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Nov. 1
In Lecture (room 4C6,10 - 11 a.m..):
- Universal central extensions and the Steinberg group
Associated Reading:
- Rosenberg, "Algebraic K-theory and its applications," Chapter 4.
- Milnor, "Algebraic K-theory," Chapter 5.
Video of class (streaming)
Video of class (downloadable)
| Nov. 3
In Lecture
- Long exact sequences in K-theory
- K_2 and symbols
Associated Reading:
- Milnor, "Algebraic K-theory," Chapters 6, 11.
- Rosenberg, "Algebraic K-theory 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 K-theory and its applications," Chapter 4.
- Milnor, "Algebraic K-theory," Chapter 5.
Video of class (streaming)
Video of class (downloadable) -
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Nov. 8
In Lecture (room 4C6,10 - 11 a.m..):
- Quillen's + construction
- Quillen's Q construction
Associated Reading:
- Rosenberg, "Algebraic K-theory 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 K-theory and its applications," Chapter 5.
Video of class (streaming)
Video of class (downloadable)
| Nov. 12
In Lecture
- End of discussion of the Q-construction
Associated Reading:
- Rosenberg, "Algebraic K-theory and its applications," Chapter 5.
Video of class (streaming)
Video of class (downloadable) -
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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 K-Theory and Classfield Theory for Arithmetic Surfaces, by Spencer Bloch Source: The Annals of Mathematics, Second Series, Vol. 114, No. 2 (Sep., 1981), pp. 229-265
- 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 K-Theory and Classfield Theory for Arithmetic Surfaces, by Spencer Bloch Source: The Annals of Mathematics, Second Series, Vol. 114, No. 2 (Sep., 1981), pp. 229-265
- 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) -
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Nov. 22
In Lecture
- Classfield theory on Curves (continued)
Associated Reading:
- Algebraic K-Theory and Classfield Theory for Arithmetic Surfaces, by Spencer Bloch Source: The Annals of Mathematics, Second Series, Vol. 114, No. 2 (Sep., 1981), pp. 229-265
- 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 K-Theory and Classfield Theory for Arithmetic Surfaces, by Spencer Bloch Source: The Annals of Mathematics, Second Series, Vol. 114, No. 2 (Sep., 1981), pp. 229-265
- 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!
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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)
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