Mathematics 256B-- Algebraic Geoemtry

MWF, 10:10--11:00, 5 Evans

Arthur Ogus

Math 256AB is a one-year sequence intending to introduce students to the basic tools and ideas of scheme theory, Grothendieck’s approach to algebraic geometry. As in Math 256A, Math 256B will mostly follow Hartshorne’s classic tex. Math 256B will begin approximately wherever Math 256A stops.The main topics will be cohomology, smoothness, and algebraic curves, with perhaps more of an emphasis on Grothendieck's functorial point of view than in the text.

Math 256B is in principle a fourth-semester graduate course, and will be run as such. Lectures may include material not in the text, and the course will move at a fairly demanding pace. Hartshorne’s text includes many excellent and challenging exercises, some of which will serve as the basis for the grading, which I hope to do in a relatively serious manner.


Other resources you may want to consult:

EGA (avialable in different formats and places in libraries and on the web)

The Stacks Project

Ravi Vakil's Notes


For information on when and how to reach me, see my home page. Typically office hours will be MWF from 2:10 till 3:00.


Course Plan


Assignment #1--due Feb. 1

Assignment #2--due Feb. 15

Notes on Assignment #2

Assignment #3--due Feb. 24

Assignment #4--due March 6

Assignment #5--due March 15

Assignment #6--due March 24 or by email on March 29

Assignment #7--due April 7

Assignmnent #8--due April 19


Differentials and Smoothness--Feb. 17

Vanishing of Cohomology--Feb. 27

The Trace Map for Projective Space--March 26

Valuation Rings

Cohomology and Base Change