Fall 2012 |

from Gathmann's notes. Due date: Monday, Oct 1.

from Gathmann's notes. Due date: Monday, Oct 22.

For 2.6.9, prove also that for every P in X the local ring is a

subring of the function field, and that if X is a variety, then

different points lead to different subrings. Moreover, prove that for

every open subset of X, the ring of regular function is the

intersection of all local rings of all its points.

4.6.2, 4.6.3, 4.6.5, 4.6.6, 4.6.7, 5.6.12

from Gathmann's notes. Due date: Friday, Nov 23.

of them each, and prepare a presentation on it. You will present them

to each other towards the end of the term, possibly in the exam

period. You should meet with me to discuss the content of your

project and the relevant literature. Some of the later topics are

more advanced and suitable for students interested in number theory.

These later subjects would be somewhat expository.

Subject | Name | Date
and Location |

Definition of elliptic curves, Weierstrass normal form. | K. Chen | Dec. 10, 3:00-4:00 Math 102 |

Classification: the j-invariant. | L. Hsu | Dec. 10, 4:00-5:00 Math 102 |

The group law. | A. Keet | Dec. 11, 3:30-4:30 Math 102 |

Elliptic functions (Elliptic curves over C). | K. Li | Dec. 11, 4:30-5:30 Math 102 |

The Picard group. | M. Bergeron | Dec. 12, 3:00-4:00 Math 102 |

Elliptic curves over finite fields (Chapter V of Silverman). | K. Behrend | Dec. 12, 4:00-5:00 Math 102 |

Mordell-Weil theorem over Q. | X. Liu | Dec. 13, 3:00-4:00 Math 102 |

Elliptic curves and congruence numbers (Chapter 1 of Koblitz). | A. Vlasev | Dec. 13, 4:00-5:00 Math 102 |

Hasse-Weil L-function of an elliptic curve. Birch-Swinnerton-Dyer conjecture. | M. Rupert | Dec. 14, 3:00-4:00 Math 102 |

Vector bundles over elliptic curves. | E. Mohyedin Kermani | Dec. 14, 4:00-5:00 Math 102 |