Timetable: Monday, Tuesday, and Wednesday, 10:00 - 11:00

Room: D1.07

Assessment: 100% Oral

Prerequisites: Assumed: commutative algebra. Useful: algebraic geometry

General information: This course will be an introduction to p-adic geometry. We will start with some brief reviews of algebraic geometry and then move on to introduce John Tate’s theory of rigid analytic spaces. Along the course, we will show how to establish a rigid analytic GAGA theorem. We will also study the relation between formal schemes and rigid analytic spaces. After learning rigid analytic spaces, we shall move on to the theory of adic spaces, which provides a foundation of Peter Scholze’s theory of perfectoid spaces.

Syllabus: 

Week 1: Introduction and review of algebraic geometry

Week 2: Some nonarchimedean analysis

Week 3: Rigid analytic space

Week 4: Coherent cohomology

Week 5: Rigid analytic GAGA

Week 6: Raynaud's theorem

Week 7: Adic spaces

Week 8: Perfectoid spaces

Week 9: Diamonds

Week 10: The Fargues--Fontaine curve

Lecture notes: Shall be updated here.

References:

1. R. Huber (1996), Étale Cohomology of Rigid Analytic Varieties and Adic Spaces

2. S. Morel (2019), Adic Spaces

3. P. Scholze and J. Weinstein (2020), Berkeley Lectures on p-adic Geometry

4. J. Tate (1971), Rigid Analytic Spaces

5. Y. Tian (2016), Introduction to Rigid Geometry

6. T. Wedhorn (2019), Adic Spaces