Spring Term 2024

Lior Silberman
- Office: MATX 1112, 604-827-3031
- Email: "lior" (at) Math.UBC.CA (please include the course number in the subject line, if applicable)
- Office hours (Fall 2024): after class (W 10:00-10:30 at the ESB atrium, W 14:00-14:30 at WW IRC Atrium), M 10:30-11:30 in my office, and by appointment.

- Classes: WF 10-11:30 at ESB 4133 and on Zoom -- see schedule below.
- Syllabus (PDF)
- (Rough) lecture notes (PDF)

- Lang, Algebraic Number Theory, available from SpringerLink
- Neukirch, Algebraic Number Theory, available from SpringerLink
- [Your favorite author], Algebraic Number Theoery

*Warning: the following information is tentative and subject to change at any time*

Chapter | Week | Date | Material | In-class | Notes |
---|---|---|---|---|---|

Intro | 1 | W 10/1 | Introduction | Scan | |

F 12/1 | Lamé's mistake | Scan | |||

Rings of Integers |
2 | W 17/1 | Algebraic integers | Scan | |

F 19/1 | Unique Factorization | Scan | |||

3 | W 24/1 | Primes in extensions | Scan | ||

F 26/1 | (continued) | Scan | |||

Local Fields |
4 | W 31/1 | Absolute values | Scan | |

F 2/2 | Completions and ${\mathbb{Q}}_{p}$ | Scan | |||

5 | W 7/2 | Complete fields | Scan | ||

F 9/2 | (continued) | Scan | |||

6 | W 14/2 | Ramification | Scan | ||

F 16/2 | (continued) | Scan | |||

Feb 19-23 | UBC Winter break | ||||

7 | W 28/2 | Places of number fields | Scan | ||

F 1/3 | (continued) | Scan | |||

Ramification | 8 | W 6/3 | Duality and the different | Scan | |

F 8/3 | (continued) | Scan | |||

9 | W 13/3 | The discriminant | Scan | ||

F 15/3 | Cyclotomic fields | Scan | |||

Geometry of Numbers |
10 | W 20/3 | Lattices | Scan | |

F 22/3 | Discriminant bounds | Scan | |||

11 | W 27/3 | Finiteness of the classgroup Dirichlet's Unit Theorem |
Scan | ||

F 29/3 | Good Friday -- no class | ||||

L-functions | 12 | W 3/4 | Smooth sums | Scan | |

F 5/4 | Analytical continuoation | ||||

13 | W 10/4 | The Dedekindzetafunction | |||

F 12/4 | Some generalizations |

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