ELLIPTIC CURVES AND IWASAWA THEORY SPRING 2006

ELLIPTIC CURVES AND IWASAWA THEORY SPRING 2006

Thursdays at 2:00 pm in 241 Altgeld Hall.

1 Jan 19 Organizational Meeting

2 Jan 26 Tim Kilbourn, "Iwasawa Theory I"
(Motivation, Main theorem, lambda,mu,nu-invariants, structure of X as Lambda module, X = inverse limit of p-class groups, Lambda = Zp[[T]])

3 Feb 2 Tim Kilbourn, "Iwasawa Theory II"
(Proof of Iwasawa's Theorem - Lambda is a Noetherian regular local ring of dimension 2, structure theorem for finitely generated Lambda modules, X is f.g. as Lambda module)

Washington, Lawrence C., Introduction to cyclotomic fields. Graduate Texts in Mathematics, 83. Springer-Verlag, New York, 1982.

Greenberg, Ralph, Iwasawa theory---past and present, Class field theory---its centenary and prospect (Tokyo, 1998), 335--385, Adv. Stud. Pure Math., 30, Math. Soc. Japan, Tokyo, 2001.

Neukirch, J"urgen; Schmidt, Alexander; Wingberg, Kay, Cohomology of number fields. Grundlehren der Mathematischen Wissenschaften 323. Springer-Verlag, Berlin, 2000.

Classical Iwasawa Theory - Jansen (Pointer)

4 Feb 9 Nadya Markin, "Realization of Nilpotent Groups with Restricted Ramification"

5 Feb 16 Radoslav Kirov, "Elliptic Curves I"
(Arithmetic of elliptic curves, formal group of an elliptic curve)

6 Feb 23 Eric Landquist, "Elliptic Curves II"
(Weak Mordell-Weil Theorem, Selmer groups and Tate-Shavarevich groups)

Silverman, Joseph H., The arithmetic of elliptic curves. Corrected reprint of the 1986 original. Graduate Texts in Mathematics, 106. Springer-Verlag, New York, 1992.

Rajan, C. S. Weak Mordell-Weil theorem. Elliptic curves, modular forms and cryptography (Allahabad, 2000), 63--72, Hindustan Book Agency, New Delhi, 2003.

Poonen, Bjorn, The Selmer group, the Shafarevich-Tate group, and the weak Mordell-Weil theorem, 2002.

7 Mar 2 Jennifer Paulhus, "Main Theorem of Complex Multiplication"

Silverman, Joseph H., Advanced topics in the arithmetic of elliptic curves. Graduate Texts in Mathematics, 151. Springer-Verlag, New York, 1994.

8 Mar 9 Bill Hart, "Elliptic Units"

Robert, Gilles, Unit'es elliptiques. (French) Bull. Soc. Math. France, M'em. No. 36. Bull. Soc. Math. France, Tome 101. Soci'et'e Math'ematique de France, Paris, 1973.

Coates, J.; Wiles, A., On the conjecture of Birch and Swinnerton-Dyer. Invent. Math. 39 (1977), no. 3, 223--251.

Rubin, Karl Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer. Arithmetic theory of elliptic curves (Cetraro, 1997), 167--234, Lecture Notes in Math., 1716, Springer, Berlin, 1999.

9 Mar 16 Bill Hart, Continued.

10 Mar 23 Spring Break

11 Mar 30 Iwan Duursma, "The one-variable Main Conjecture"

12 Apr 6 Jonathan Webster, "Iwasawa modules and p-adic L-series"

13 Apr 13 Steve Ullom, "Tools from Iwasawa Theory"

14 Apr 20

15 Apr 27

16 May 4

1	Jan 19	Organizational Meeting
2	Jan 26	Tim Kilbourn, "Iwasawa Theory I" (Motivation, Main theorem, lambda,mu,nu-invariants, structure of X as Lambda module, X = inverse limit of p-class groups, Lambda = Zp[[T]])
3	Feb 2	Tim Kilbourn, "Iwasawa Theory II" (Proof of Iwasawa's Theorem - Lambda is a Noetherian regular local ring of dimension 2, structure theorem for finitely generated Lambda modules, X is f.g. as Lambda module)
		Washington, Lawrence C., Introduction to cyclotomic fields. Graduate Texts in Mathematics, 83. Springer-Verlag, New York, 1982. Greenberg, Ralph, Iwasawa theory---past and present, Class field theory---its centenary and prospect (Tokyo, 1998), 335--385, Adv. Stud. Pure Math., 30, Math. Soc. Japan, Tokyo, 2001. Neukirch, J"urgen; Schmidt, Alexander; Wingberg, Kay, Cohomology of number fields. Grundlehren der Mathematischen Wissenschaften 323. Springer-Verlag, Berlin, 2000. Classical Iwasawa Theory - Jansen (Pointer)
4	Feb 9	Nadya Markin, "Realization of Nilpotent Groups with Restricted Ramification"
5	Feb 16	Radoslav Kirov, "Elliptic Curves I" (Arithmetic of elliptic curves, formal group of an elliptic curve)
6	Feb 23	Eric Landquist, "Elliptic Curves II" (Weak Mordell-Weil Theorem, Selmer groups and Tate-Shavarevich groups)
		Silverman, Joseph H., The arithmetic of elliptic curves. Corrected reprint of the 1986 original. Graduate Texts in Mathematics, 106. Springer-Verlag, New York, 1992. Rajan, C. S. Weak Mordell-Weil theorem. Elliptic curves, modular forms and cryptography (Allahabad, 2000), 63--72, Hindustan Book Agency, New Delhi, 2003. Poonen, Bjorn, The Selmer group, the Shafarevich-Tate group, and the weak Mordell-Weil theorem, 2002.
7	Mar 2	Jennifer Paulhus, "Main Theorem of Complex Multiplication"
		Silverman, Joseph H., Advanced topics in the arithmetic of elliptic curves. Graduate Texts in Mathematics, 151. Springer-Verlag, New York, 1994.
8	Mar 9	Bill Hart, "Elliptic Units"
		Robert, Gilles, Unit'es elliptiques. (French) Bull. Soc. Math. France, M'em. No. 36. Bull. Soc. Math. France, Tome 101. Soci'et'e Math'ematique de France, Paris, 1973. Coates, J.; Wiles, A., On the conjecture of Birch and Swinnerton-Dyer. Invent. Math. 39 (1977), no. 3, 223--251. Rubin, Karl Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer. Arithmetic theory of elliptic curves (Cetraro, 1997), 167--234, Lecture Notes in Math., 1716, Springer, Berlin, 1999.
9	Mar 16	Bill Hart, Continued.
10	Mar 23	Spring Break
11	Mar 30	Iwan Duursma, "The one-variable Main Conjecture"
12	Apr 6	Jonathan Webster, "Iwasawa modules and p-adic L-series"
13	Apr 13	Steve Ullom, "Tools from Iwasawa Theory"
14	Apr 20
15	Apr 27
16	May 4