##
September 2015 version

Posted by ravivakil under

2015-16 course,

Actual notes
[3] Comments
The September 2015 version is in **the usual place**. I’m posting it because our academic year is just starting, and I will be teaching Math 216 again; this year’s course website is **here**.

The list of intended changes and corrections has grown again, but essentially all are small. My intent is to try to have the changes and corrections in each chapter digested as much as possible before the courses reaches there.

The one bit of potentially new content: David Speyer pointed out that Grobner bases are something that people could and should reasonably see in a first course. Over lunch in Utah, I thought it through with him and Kiran Kedlaya and Tom Graber. I will likely post a draft here before thinking about whether to including it.

October 10, 2015 at 7:43 am

In the statement of 24.5.B(b) it doesn’t seem true that having all is the same as being supported everywhere if $M$ isn’t finitely generated. I think something like and exhibits this. Hopefully I’m not wrong.

October 12, 2015 at 5:12 am

No, you are right! Now fixed.

October 20, 2015 at 12:06 am

There seems to be a slight misstatement in the aside to the proof of Theorem 4.1.2 (sheaf-on-a-base conditions in the initial definition of the structure sheaf of an affine scheme) that deals with the equalizer exact sequence interpretation of those conditions.

As currently stated, sequence (4.1.3.1) doesn’t appear to necessarily be exact. (I think taking , , gives a counterexample, as we have that .)

I imagine what you mean is to induce the map in sequence (4.1.3.1) from the maps , given by the difference between the two “obvious” ones through and respectively rather than just one of them (or its negative). This would allow the two “obvious” maps to cancel each other out in the same coordinate when applied to the image of an element of in , so that the th and th coordinates are each equal to zero rather than just summing to zero. (It also gets rid of the need to arbitrarily specify an order on : in the th coordinate, simply take the one through minus the one through , rather than only going through and possibly negating depending on the relative order of and .)