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Introduction to rigid analytic geometry-Adic spaces and applications

External Lecturer: 
Alberto Vezzani
Course Type: 
PhD Course
Academic Year: 
2022-2023
Duration: 
20 h
Description: 

The course is an introduction to some of the newest approaches to non-archimedean analytic geometry including:- Huber's adic spaces;- Raynaud's formal schemes and blow-ups;- Clausen-Scholze's analytic spaces.We will focus on specific examples arising from algebraic geometry, Scholze's tilting equivalence of perfectoid spaces and the Fargues-Fontaine curve.We will also show how to define (motivic) homotopy equivalences in this setting, with the aim of defining a relative de Rham cohomology for adic spaces over $\mathbb{Q}_p$  and a relative rigid cohomology for schemes over  $\mathbb{F}_p$. 

Location: 
A-136
Location: 
The alternative lecture room is A-005.
Next Lectures: 

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