Lecture 36 (December 11): étale cover of the moduli space of curves Lecture 35 (December 9): Artin approximation Lecture 34 (December 6): Artin approximation Lecture 33 (December 4): Artin approximation Lecture 32 (December 2): proof of N7eacute;ron desingularization Lecture 31 (November 25): proof of Néron designularization
Suggested reading: Néron models, §§3.1–3.4 Lecture 30 (November 22): defect of smoothness Lecture 29 (November 20): induction setup for smoothening Lecture 28 (November 18): algebraization of formal curves, smooething Lecture 27 (November 13): infinitesimal deformation of invertible sheaves Lecture 26 (November 11): Grothendieck's existence theorem Lecture 25 (November 8): theorem on formal functions Lecture 24 (November 6): infinitesimal structure of the moduli space of curves Lecture 23 (November 4): the moduli space of curves is homogeneous Lecture 22 (November 1): tangent spaces of fibered categories, homogeneity Lecture 21 (October 30): openness of ampleness, the moduli space of curves is a stack Lecture 20 (October 28): local finite presentation of the moduli space of curves, openness of ampleness on the base Lecture 19 (October 25): more local finite presentation Lecture 18 (October 23): local finite presentation Lecture 17 (October 21): formal smoothness of the moduli space of curves Lecture 16 (October 18): fiber criterion for smoothness Lecture 15 (October 16): equivalence of differential and infinitesimal criteria, étale morphisms are flat Guest Lecture (October 11): Dan Abramovich Guest Lecture (October 9): Sebastian Bozlee Lecture 14 (October 4): differential criteria and equivalence with infinitesimal criteria Lecture 13 (October 2): review of derivations and differentials, formal criteria for smooth, étale, unramified
Suggested reading: Néron models, §§2.1–2.2 Lecture 12 (September 30): moduli of curves as a stack Lecture 11 (September 27): examples of fpqc descent (Galois theory, coherent sheaves on projective space, moduli of curves) Lecture 10 (September 25): proof of fpqc descent Lecture 9 (September 23) Lecture 8 (September 20) Lecture 7 (September 18): closed embeddings in terms of functors, overview of fpqc descent
Suggested reading: Algebraic spaces and stacks, §§4.1–4.3 by Olsson
Suggested reading: Notes on Grothendieck topologies, fibered categories, and descent theory, §4.2 by Vistoli
Suggested reading: Néron models, §6.1, by Bosch, Lütkebohmert, and Raynaud Lecture 6 (September 16): projective space as a fibered category and the definition of a stack
Suggested reading: Notes on Grothendieck topologies, fibered categories, and descent, Chapter 3, by Angelo Vistoli (appears in FGA Explained) Lecture 5 (September 13): moduli of triangles as a fibered category the moduli space of oriented metric triangles Lecture 4 (September 11): fibered categories and stacks
Reading suggestion: Stacks for everybody by Barbara Fantechi Lecture 3 (September 9): the functor of points of projective space Lecture 2 (September 6): introduction and functors of points Lecture 1 (September 4): introduction