Graduate Algebra; 506A

Instructor: Julia Pevtsova

Place: Padelford Hall, C36

Time: 9:30-10:20, MWF

Office Hours: by appointment (that is, I am happy to talk between classes, just need an advance notice)

 

Course Description.  The main emphasis this quarter will be on commutative algebra.  We shall cover Hilbert’s Nullstellesatz, prime ideal spectrum and Zariski topology, localization, tensor product, flatness, exterior and symmetric powers, discrete valuations and Dedekind rings, projective and injective modules, Tor and Ext. Time permitting we may do some representation theory.

 

Texts. 

More references.

·         Introduction to algebraic geometry:  Undergraduate Algebraic Geometry, M. Reid;  Algebraic Geometry, R. Hartshorne (classical reference)

·         Introduction to homological algebra: Homological algebra, H. Cartan, S. Eilenberg; An Introduction to Homological Algebra, C.Weibel; Methods of Homological Algebra, S. Gelfand, Yu. Manin; Basic Homological algebra, M.S. Osborne

Gradinhg system.  Grades will be determined based on homework assignments, a midterm and a final as follows:

·         Homework 40%

·         Midterm 20%

·         Final 40%

Midterm will be given on Monday, May 4th. Please plan accordingly.

Final exam is Wednesday, June 10th, at 8:30am

 

Homework. Assignments will be posted on this website on a weekly basis. You are encouraged to tex your homework especially if you did not take a calligraphy course in the past.

 

Homework 1, due Friday, April 10

Additional problems 1 (optional, but useful)

Homework 2, due Friday, April 17, last updated Wed, April 15 (problem 6 moved to HW3)

            Some solutions: Problem 1a), Problem 5 (courtesy of Chris Aholt)

Homework 3, due Friday, April 24, final version, posted Friday, April 17

Additional problem 3

Homework 4, due Monday, May 4 (new due date!).  PDF file, TEX file.  Corrected version posted Tuesday, April 28th.

Midterm and some solutions (posted May 7th).

Homework 5, due Friday, May 15. PDF file, TEX file.

Homework 6, due Friday, May 22. PDF file, TEX file.

Homework 7, due Friday, May 29. Corrected version posted Sunday, May 24th.

Homework 8, due Friday, June 5.  There are 2,5 optional problems which you don’t have to turn in. One may be useful as part of the review for the final, another is more of a prelim type problem on representation theory.

Final and solutions, June 10.

 

HAVE A GOOD SUMMER!