Welcome to the NYU Algebraic and Analytic Geometry Seminar webpage! The purpose of the seminar this semester is to introduce students to Serre's GAGA, not necessarily talk about recent research in the field. The prerequisites for this seminar are a solid understanding of complex analysis and algebra. We will introduce schemes and sheaf cohomology.
Leaders: Jacob Monzel and Jake Zweifler
Emails: [email protected] and [email protected]
Class: Tuesdays 4:00-5:00pm (WWH 605)
References: Algebraic and Analytic Geometry by Neeman (our main reference), Hartshorne, Görtz-Wedhorn
| Week | Topic | Reading | Paper/Notes/Problem/Remarks |
|---|---|---|---|
| Syllabus Week | Introductory Meeting | None | We planned to skim NeemanChap10 and review NeemanChap2 for next week. We changed the meeting time to 4-5pm. (PDFs removed) |
| 1 | Manifolds | Chapter 2 | We went over chapter 2 in Neeman and outlined the main proof of GAGA. (PDFs removed) |
| 2 | Schemes | Chapter 3 | We went over the basics of scheme theory and schemes of finite type over C. (PDFs removed) |
| 3 | The Complex Topology | Chapter 4 | We reviewed the complex topology and Max(X) of a space. (PDFs removed) |
| 4 | The Analytification of a Scheme | Chapter 5 | PDFs removed |
| 5 | The High Road to Analytification | Chapter 6 | PDFs removed |
| 6 | Coherent Sheaves | Chapter 7 | PDFs removed |
| 7 | Projective Space | Chapter 8 | PDFs removed |
| 8 | Projective Space | Chapter 9 | PDFs removed |
| 9 | Proof of GAGA | Chapter 10 | PDFs removed |
| 10-15 | Buffer Week | Buffer Week | PDFs removed |