Complex analytic spaces, vector bundles, and GAGA

Abstract: Definition of the category of complex analytic spaces, and statements of GAGA.

References:

• Hartshorne, Algebraic geometry, 1977. Appendix B.1 and B.2.
• Gunning and Rossi, Analytic functions of several complex variables, Prentice-Hall (1965).
• Serre, Géometrie algébrique et géometrie analytique, Ann. Inst. Fourier 6 (1956), 1-42.
• Grothendieck, SGA I, Exp. XII

algebraic geometrynumber theory

Audience: advanced learners

STAGE

Series comments: STAGE (Seminar on Topics in Arithmetic, Geometry, Etc.) is a learning seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.

Fall 2025 topic: Weil conjectures.

Some topics might take more or less time than allotted. If a speaker runs out of time on a certain date, that speaker might be allowed to borrow some time on the next date. So the topics below might not line up exactly with the dates below.