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