Rigid Analtyic Geometry and Perfectoid Spaces
We will be covering the basics of Rigid Analytic Geometry in the first half of the seminar, then moving onto adic and perfectoid spaces. Our main source for the first half will be [B]. After this, we will likely follow [C].

When: Wednesday 6:00pm  7:30pm ET

Where: Math 528  or by Zoom

References:

[B] Bosch Lectures on Formal and Rigid Geometry

[C] Conrad ,

Any notes taken will be added here.
Schedule

September 14

Alex Scheffelin

What is Rigid Geometry and Tate Algebras (Chapters 1 & 2 of [B])
We will discuss what rigid geometry is, and begin by introducing the notion of a Tate algebra, a fundamental notion in rigid geometry.


September 21

Alex Scheffelin

Finishing Tate Algebras (Chapter 1 of [B])

We will finish our exposition of chapter 2, completing proofs of several elementary facts about Tate algebras, and then proving that ideals are complete, and thus closed.


Notes for 14th and 21st: notes


September 28

Kevin Chang

Affinoid Algebras and Affinoid Spaces (Sections 3.1 & 3.2 of [B])
We will introduce an affinoid algebra, which is the rigid analog of a finite type Kalgebra.
We also introduce Sp A, the affinoid Kspace associated to A which plays a role analogous to Spec
in algebraic geometry.


October 5

Benjamin Church

Affinoid Subdomains (Section 3.3 of [B])
The Zariski topology on an affinoid Kspace is coarse. We will introduce a finer
topology which is induced directly from K's topology.