Course:MATH600D 17/18-II

From UBC Wiki
Jump to: navigation, search
Faculty of Science
Department of Mathematics
Wind colours.jpg
MATH 600 / D
Topics in Algebra
Instructor: Sujatha Ramdorai
email
Office: MATH Annex 1201
Class schedule: Tue Thu<br\>11:00 am - 12:30 pm
Classroom: MATH Annex 1102
Office hours:
Course pages
No pages found.


In this course, we plan to cover some parts of Commutative Algebra that are used in Algebraic Number Theory and Algebraic Geometry. Some of these topics will include Integral closure, Dedekind domains and Discrete valuation rings. We will then cover some ground from Homological Algebra, primarily leading to the concept of homological dimension of Noetherian rings. This will be used to state the Auslander-Buchsbaum Theorem on regular local rings and provide an overview of key steps in the proof. The aim is to make the course as self-contained as possible. Students are definitely expected to be familiar with the material covered in Algebra I (Course no. 501). Some exposure to Homological Algebra will be helpful, though not strictly necessary. Grades will be based on class participation, engagement, exercises and lectures. The participants are expected to give one or two lectures along the course. There is no prescribed text book. The books listed in the References section will be helpful for the students

Homework

Student Lectures

Lecture Details

Lecture<br\>Date Topics Covered Notes
1
4/1
Integral Extensions Class 1 notes
2
9/1
Integral Extensions (contd.)
3
11/1
Norms and Traces, Spectrums of Int. Extns
4
16/1
Height, Dimension and Localization
5
18/1
Projective Dimension, Going Up and Down
6
23/1
Going Down (contd.), Flat Extensions
7
25/1
8
30/1
UFDs
9
1/2
Discrete Valuation Rings; Noetherian Modules (Coco's talk) Coco's talk
10
6/2
Normal and Dedekind domains
11
8/2
Projective and Flat Modules: Coco and Ashvni

References

  • M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra. Addison-Wesley Publishing Company, Inc.
  • H. Matsumara, Commutative Algebra. W.A. Benjamin.
  • E. Kunz, Introduction to Commutative Algebra and Algebraic Geometry. Springer.
  • C. Weibel, An Introduction to Homological Algebra. Cambridge University Press.
  • TIFR Pamphlet on Homological Algebra