External Lecturer:
Alberto Vezzani, Universita' degli Studi di Milano
Course Type:
PhD Course
Academic Year:
2022-2023
Duration:
20 h
Description:
Abstract:
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}_pand a relative rigid cohomology for schemes over \mathbb{F}_p.
- 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}_pand a relative rigid cohomology for schemes over \mathbb{F}_p.
Zoom link:
Topic: Rigid geometry Milano-SISSA
Time: This is a recurring meeting Meet anytime
Time: This is a recurring meeting Meet anytime
Join Zoom Meeting
https://us02web.zoom.us/j/82357041692?pwd=bEFUZmI1dUlCT0J0c2s5THRwZ09LUT09
Meeting ID: 823 5704 1692
Passcode: 725699
Research Group:
Location:
Online