We'll have a weekly discussion of a classic paper in number theory. Ideally this seminar should be very participatory; read over the paper ahead of time and come prepared with questions for optimal results.

Here's the list of papers (in no particular order) that have been suggested; feel free to email me with suggestions if you'd like to hear about/talk about something not on this list.

- Elkies:
*The existence of infinitely many supersingular primes for every elliptic curve over Q*. - Swinnerton-Dyer:
*On l-adic representations and congruences for coefficients of modular forms*, Serre:*Congruences et formes modulaires*. - Lenstra:
*Factoring integers with elliptic curves*. - Serre:
*Sur les représentations de degré 2 de Gal(Qbar/Q)*. - Stark: papers on the class number 1 problem for imaginary quadratic fields, see
*A complete determination of the complex quadratic fields of class number one*and*On the 'gap' in a theorem of Heegner*. - Gross:
*a tameness criterion for Galois representations associated to modular forms (mod p)*. - Fontaine:
*Il n'y a pas de variété abélienne sur Z*. - Larsen-Pink: papers on compatible systems, see
*On l-independence of algebraic monodromy groups in compatible systems of representations*and*Abelian varieties, l-adic representations, and l-independence*. - Serre-Tate:
*Good reduction of abelian varieties*. - Honda-Tate: see Tate's
*Classes d'isogénie des variétés abéliennes sur un corps fini (d'après T. Honda)*and Honda's*Isogeny classes of abelian varieties over finite fields*. - Mazur-Tate:
*Points of order 13 on elliptic curves*.

The seminar meets 3:45-5:00 on Tuesdays in the barn (Ryerson 352).

Date | Speaker | Paper |
---|---|---|

April 10 | Karl | Elkies: The existence of infinitely many supersingular primes for every elliptic curve over Q. |

April 17 | No meeting this week. | |

April 24 | Billy | Swinnerton-Dyer: On l-adic representations and congruences for coefficients of modular forms, Serre: Congruences et formes modulaires. |

May 1 | John | Serre-Tate: Good reduction of abelian varieties. |

May 8 | Eric | Tate: The non-existence of certain Galois extensions of Q unramified outside 2. |

May 15 | Bingjin | Fontaine: Il n'y a pas de variété abélienne sur Z. |

May 22 | Mathilde | Eskin, Rudnick, Sarnak: A proof of Siegel's weight formula. |

May 29 | Nazerke | Serre: Sur les représentations de degré 2 de Gal(Qbar/Q). |