Commutative and Multilinear Algebra, Semester 1, 2016

Class: Tue 3:15 Thu 2:15 Fri 10:00 Williams Theatre

Office hours: Tue 4:15 5:45, Fri 11:00-12:30 Richard Berry 169

Schedule

Lecture Date Summary Homework Suggested reading
1 01/03 Tensor product of modules Review definition, brush up on categories and functors Wikipedia or Bourbaki, MacLane (categories), Taufik also recommends the book by Goldblatt on topoi.
2 03/03 Tensor products of modules, continued Work through the list of examples from class
3 04/03 Symmetric and exterior powers
4 08/03 Determinants Consolidate our definition with the one you knew defintion of determinant in linear algebra
5 10/03 Manifolds, tangent and cotangent vectors, 1-forms
6 11/03 A slower review of the material of Thursday's class Spivak, Galot-Hulin-LaFontaine
7 15/03 Kaehler differentials Matsumura
8 17/03 Kaehler differentials, continued Matsumura
9 18/03 prime ideals and maximal ideals Atiyah and Macdonald
10 22/03 Jacobson and Nilradical Atiyah and Macdonald
11 24/03 The prime spectrum of a ring Assignment 1 due Tuesday 12/04 Solutions Atiyah and Macdonald
12 05/04 Localisation Atiyah and Macdonald
13 07/04 Local properties Atiyah and Macdonald
14 08/04 Localisation, contraction and extension of ideals Atiyah and Macdonald
15 12/04 Localisation, contraction and extension of ideals Atiyah and Macdonald
16 14/04 Localisation, contraction and extension of ideals Atiyah and Macdonald
17 15/04 Primary ideals Atiyah and Macdonald
18 19/04 Primary decomposition Atiyah and Macdonald
19 21/04 Primary decomposition Atiyah and Macdonald
20 22/04 Primary decomposition, first uniqueness theorem Atiyah and Macdonald
21 26/04 Primary decomposition, second uniqueness theorem Atiyah and Macdonald
22 28/04 Integral dependence Assignment 2 due Tuesday 10/05 in class Atiyah and Macdonald
23 29/04 Going-up Atiyah and Macdonald
24 03/05 Starting to go down Atiyah and Macdonald
25 05/05 Going down Atiyah and Macdonald
26 06/05 Going down Atiyah and Macdonald
27 10/05 Zariski's Lemma implies the Nullstellensatz Wikipedia
28 12/05 Valuation rings Atiyah and Macdonald
29 13/05 Valuation rings Atiyah and Macdonald
30 17/05 Proof of Zariski's Lemma Assignment 3, due on Friday, 27 May, consists of the exercises 1, 10 -- 14 and 28 in Chapter 5 of Atiyah Macdonald. Atiyah and Macdonald

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