Reference for Deligne-Mumford

Question

What is a good reference for someone new to the theory of Deligne-Mumford stacks, other than the original Deligne-Mumford paper itself? The paper itself seems readable with some effort; but the fear is that the reader will miss out on whatever happened in the later years. Is there a good introduction at the graduate level?

Answer 1

There is the book of Laumon and Moret-Bailly.

There is of course the stacks project.

There are also Artin's paper on algebraic spaces (his survey on the implicit function theorem in algebraic geometry from the Bombay conference, and also his two papers on algebraization of formal moduli). When I was recently trying to learn this material, I found Artin's papers very helpful, even though they are about algebraic spaces rather than stacks proper.

Answer 2

You can take a look at the notes by Daniel Halpern-Leistner which can be found at

http://pi.math.cornell.edu/~danielhl/moduli_theory_notes.pdf