Schedule
| Sep 5 |
Chap 0 Milne, p. 1-5
| | Sep 12 |
Profinite groups; infinite galois theory;
Formulation of LCFT Milne chap 1.
| | Sep 19 |
Due date Homework 1:
Choose 4 exercises from 1.9 through 1.18 of Lenstra's text
Galois theory for schemes [PDF]
Erratum: $R\times R$ should be $RxR$ in 1.18 (a)
Solutions [PDF]
| | Sep 26 |
Chap 1, section 2,3 of Milne. See also
Chapter 8 [PDF] of Fesenko's
book.
| | Oct 3 | No class
| | Oct 10 |
Finish Chap 1, §3
Due date Homework 2:
Choose 2
of the exercises 1-6 of Section 1
of
Chapter 8 [PDF] of Fesenko's
book
and choose 2 exercises out of
2.3, 2.10, 2.11, 2.13 in Lenstra's text
Galois theory for schemes [PDF].
Solutions [PDF]
| | Oct 17 |
Chap 2: Cohomology groups, bar-resolution
| | Oct 24 | No class
| | Oct 31 |
Derived functors, ext and tor, and Tate cohomology groups,
| | Nov 7 |
Inflation and restriction,
Cohomology of cyclic groups, H_1(G,Z), cupproduct
Homework 3: Choose 4 exercises from
o3.pdf.
Solutions [PDF]
| | Nov 14 |
Herbrand quotient,
Tate's theorem (part 1), cohomology of profinite groups
| | Nov 21 |
Tate's theorem (part 2), cohomology of local units in the unramified case
| | Nov 28 |
Proof of the main results
| | Dec 5 |
Proof of the main results
Homework 4: do all 4 exercises of o4.pdf.
Solutions [PDF]
| | Dec 12 |
Hilbert symbol
| | Dec 19 |
Global class field theory
Due date Homework 5:
do 4 of the 5 exercises of o5.pdf.
Solutions [PDF]
|
Last update January 30, 2012, 18:29 |