Math 664: Algebraic Geometry 2.

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Catalog Information

Title

Algebraic Geometry 2.

Credit Hours

3

Prerequisite

Math 676 or concurrent enrollment.

Description

Cohomology of schemes. Classification problems. Applications.

Desired Learning Outcomes

Prerequisites

Math 663

Minimal learning outcomes

As this is a terminal course, the instructor has freedom to choose the topic. One possibility is to study local properties of schemes. Here are the outcomes for such a course.

Students should achieve mastery of the topics listed below. This means they should know all relevant definitions, correct statements of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving non-trivial problems related to these concepts, and by proving simple (but non-trivial theorems about the concepts below, related to, but not identical to, statements proven by the text or instructor.

  • Quasi-coherent sheaves
    • Nonsingularity and differentials
    • Etale morphisms
    • Uniformizing parameters
    • Normal varieties and normalization
    • Zariski's main theorem
    • Flat and smooth mrophisms

Additional topics

Courses for which this course is prerequisite