So I was asked today if all of the “omitted” proofs and explanations in the stacks project are supposed to be filled in. The answer is: Yes, they are!

Since my goal was to build enough theory to get to the more advanced material on algebraic spaces and algebraic stacks, I have not always filled in all the proofs in the earlier parts. On the other hand, I claim that what I omitted is consistently of a relatively low difficulty (provided you read the definitions, and understand the material generally speaking). Of course my judgment could have been off and if you find a more difficult omitted proof or something you don’t understand, then please email stacks.project@gmail.com.

Now if you are an undergraduate or graduate student, then this is a perfect opportunity to hone your algebraic geometry skills. The key word to search for in the documents or in the book is “omit” (case insensitive). Find a spot where the proof is missing and you feel comfortable filling it in. Write up the proof (with references only to other results in the stacks project) and email the tex file to the address mentioned above. Your writeup will be reviewed and perhaps edited, and then added to the stacks project.

A quick search through the tex files in the stacks project shows there are 740 occurrences of the stem “omit”. So there are many things you can do!

And before somebody asks: All errors are supposed to be fixed. So email any typos, misspellings, mistakes, arrows pointing the wrong way, etc to the email address above. Don’t wait, just send any you find right away.