Algebraic Number Theory 2026

Week 1, February 17th: Integers, finite fields, Legendre symbol.
Sections: 1.1.1 - 1.1.5.
Recommended exercises: 1.1, 1.2, 1.4, 1.5, 1.6, 1.7.
Optional exercises: 1.3, 1.8, 1.9.

Week 2, February 24th: Gaussian integers, PIDs, factorial rings.
Sections: 1.2.1 - 1.2.4.
Recommended exercises: 2.1, 2.2, 2.3, 2.4.
Optional exercises: 2.7.

Week 3, March 3rd:  Euclidean rings, localisations, rings of integers.
Sections: 1.2.5 - 1.3.2.
Recommended exercises: 2.5, 2.6, 2.8, 2.9, 3.1, 3.2, 3.3.
Optional exercises: 2.10, 3.4, 3.5.

Week 4, March 12th:  DVRs, Dedekind domains.
Sections: 1.3.2 - 1.3.4.
Recommended exercises: 3.6, 3.8.
Optional exercises: 3.7.

Student presentation #1:
Topic: Primes of the form x^2 + 2y^2.
Presenter: Enzo Plauzoles.

Week 5, March 18th: Number rings, integers in quadratic fields.
Sections: 1.3.4 - 1.3.6.
Recommended exercises: 3.9, 3.11, 3.12, 3.14, 3.15, 3.16.
Optional exercises: 3.10, 3.13.

Student presentation #2:
Topic: Primes of the form x^2 + 3y^2.
Presenters: Ruben de Paiva Mota & Noa Reichert.

Week 6, March 25th: Invertible ideals, Picard and class groups.
Sections: 2.1.1 - 2.1.2.
Recommended exercises: 2.1, 2.3, 2.5, 2.6.
Optional exercises: 2.4.

Week 7, April 1st: Norms of ideals, the Kummer-Dedekind theorem.
Sections: 2.1.3 - 2.1.4.
Recommended exercises: 2.2, 2.8, 2.9.
Optional exercises: 2.7.

Student presentation #3:
Topic:  The equation x^3 = y^2 + 5.
Presenters: Pierre Foxius & Nadine Haas.

Week 8: No class

Week 9, April 13th: 
Sections: 2.1.4 - 2.1.5.
Recommended exercises: 2.13, 2.14, 2.15.
Optional exercises: 2.10.

Week 10, April 22nd:
Sections: 2.1.5 - 2.1.6.
Recommended exercises: 2.11, 2.12, 2.17.
Optional exercises: 2.16.

Student presentation #5:
Topic:  The equation x^2 + 5y^2.
Presenters: Janina Płaneta & Naki Şengezer.

Week 11, April 29th:
Sections: 2.1.6 - 2.2.1.
Recommended exercises: 2.1, 2.3.
Optional exercises: 2.2.

Student presentation #6:
Topic:  The equation x^2 + 6y^2.
Presenters: Zaccarie Belfki & Samuel Nigro.

Week 12, May 5th + May 6th:
Sections: 2.2.1 - 2.2.2.
Recommended exercises: 2.5, 2.7, 2.8.
Optional exercises: 2.4.

Student presentation #7:
Topic:  The equation x^2 + 30y^2.
Presenters: Filipa Gonçalves Marques & Sanny Schwartz.

Week 13, May 13th:
Sections: 2.2.3 - 2.2.4.
Recommended exercises: 2.6, 2.9.
Optional exercises: 2.10.

Student presentation #8:
Topic:  Prime generating polynomials.
Presenters: Jie Chen, Selma Hamzaj & Michel Tinlé Sadler.

Week 14: No class 

Week 15, May 27th:
Sections: 2.2.5 - 2.2.6.
Recommended exercises: 2.15, 2.16, 2.17, 2.18, 2.19, 2.20.
Optional exercises: 2.11, 2.12, 2.13, 2.14.

Student presentation #9:
Topic:  A complicated cubic field.
Presenters: Noa Reichert & Tom Sachsen.