This page is here just to provide a pointer to the page for the 2015-16 course.  (You can also click on the tab above.)

Following my goal of posting current versions every month, the November 28, 2015 version is in the usual place. There are many small changes, but nothing that should particularly make you want to download it.

As always, I have a big list of emails, responses, etc. that I want to respond to, and a number I intend to respond to fairly soon.

Following my goal of posting current versions every month, the October 24, 2015 version is in the usual place.  There are many small changes, but nothing that should particularly make you want to download it.

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.

My hope of a new version each month has clearly not worked out! But here is one for April, just before the month ends. As usual, a random selection of corrections and minor improvements have been dealt with, and many more remain to do.

The April version is posted at the usual place (the April 29, 2015 version).

I am going to attempt to put up a version every month, in order to ensure that I continue to spend a little time tidying things up every so often.  So the January version is now  posted at the usual place (the January 29, 2015 version, also in e-reader format).

The list of things to do has shrunk, but there is a good deal still to do.  I have had many useful detailed comments to later digest and then include from Gurbir Dhillon, Tony Feng, Lisa Sauermann, and Jesse Silliman; and Benjamin Ljundberg, Chandrasekhar Raju, and Scott Zhang.


The last version posted was in 2013. I wanted to get the next version out in 2014, and time is running out!  So here it is, posted at the usual place (the Dec. 30, 2014 version).  (There is also a version suited for an e-reader — thanks to Jack Sherk asking for it, and explaining to me how to make it.)

In this 2014 post, I can’t help mentioning the passing of Grothendieck.   I was more moved than I expected to hear the news and feel the ripples in the mathematical community.  It feels strange that he is now a historical figure, even though he had walked away from his unfinished cathedral long before I was even aware of its existence.

The notes have continued to evolve around the edges, although the material is stable. Please continue to give me corrections and suggestions!  There are few sections that need tender loving care; I mention them on the front.  There are many other things on my to-do list as well, including many comments you’ve made.

The notes now have a tentative title (The Rising Sea:  Foundations of Algebraic Geometry).  The phrase is due to Grothendieck, translated by Colin McLarty; it is the title of Daniel Murfet’s wonderful blog.

The index is in the process of being made.  (No need to give me specific comments until it has converged!)

Finally, if you would like notes on commutative algebra that are very much from the same point of view as these notes, you may enjoy Andy McLennan’s notes, available here.  It also contains an (explicated) English translation of Serre’s epochal FAC, and all the algebra needed as background.


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