Workshop on Synthetic Algebraic Geometry

University of Gothenburg/Chalmers
March 11-15, 2024

Other SAG meetings


Synthetic algebraic geometry is the study of algebraic geometry by synthetic means - instead of building up everything from ZF(C), we reason internally to a topos which contains the objects of interest. This topos is called the higher Zariski topos and is given by higher Zariski-sheaves on affine schemes of finite type over an arbitrary base ring. Higher sheaves are neccessary to interpret homotopy type theory. This provides us with an easy access to cohomology groups.

If you like to know more about synthetic algebraic geometry you can check out this hottest-talk, the website of the last meeting or you can go directly to the youtube-playlist of this meeting. An overview of the results and subtopics of synthetic algebraic geometry is on github.


recordings (Youtube-Playlist)

Time Mon Tue Wed Thu Fri
9:30 - 10:30 Overview Models of SAG Light Condensed Types Étale Sheaves Intro to A1-homotopy theory
11:00 - 12:00 Affine Schemes Cohomology I Relation to Synthetic Differential Geometry Automorphisms of Projective Space A1-homotopy groups
14:00 - 15:00 Schemes Cohomology II Excursion Intersection theory (with working session) Discussion: Open Problems
15:30 - 16:30 Exercises Towards Synthetic Riemann-Roch Excursion Formally étale types Discussion: Names (TBC)

(On Friday we did not really follow the usual pattern - we had some short discussions with presentations and later in the day groups worked independently)

Research Talks

Topic Speaker
Towards Synthetic Riemann-Roch Xuanrui Qi
Automorphisms of Projective Space Thierry Coquand
Light Condensed Types Freek Geerligs
Relation to Synthetic Differential Geometry Ulrik Buchholtz
Étale Sheaves Hugo Moeneclaey
Intersection theory (with working session) Marc Nieper-Wißkirchen
Intro to A1-homotopy theory Felix Cherubini
A1-homotopy groups Hugo Moeneclaey
Formally étale types Mark Williams
Note on reduced schemes Marc Nieper-Wißkirchen

Introductory Talks

Topic Speaker
Overview, Cohomology I and maybe Cohomology II Felix Cherubini
Affine Schemes David Wärn
Schemes, Exercises Hugo Moeneclaey
Models of SAG Thierry Coquand


Don't be confused: There are two universities, Chalmers and the University of Gothenburg. The Computer Science and Engineering (CSE) department is shared between the two universities.
The meeting will be in the CSE department in Johanneberg, Gothenburg.

Room EL41 in the EDIT building, Rännvägen 6 in Gothenburg.
The position is marked on the map below - there are also marks in red for lunch and dinner options.


Andreas Abel University of Gothenburg
Daniel Apol University of Gothenburg
Heiko Braun University of Bonn
Ulrik Buchholtz University of Nottingham
Evan Cavallo University of Gothenburg
Felix Cherubini University of Gothenburg
Thierry Coquand University of Gothenburg
Fabian Enders University of Augsburg
Esther Galby University of Gothenburg
Freek Geerligs University of Gothenburg
Jonas Höfer University of Gothenburg
Joost Hooyman University of Bologna
Chonghan Li Chalmers
Tim Lichtnau University of Bonn
Nico Lorenz University of Bochum
Adrien Mathieu ENS Ulm
Hugo Moeneclaey University of Gothenburg
Marc Nieper-Wißkirchen University of Augsburg
Kanstantsin Nisht Chalmers
Xuanrui Qi Nagoya University
Christian Sattler University of Gothenburg
Lukas Stoll University of Augsburg
David Wärn University of Gothenburg
Mark Williams University of Nottingham
Lingyuan Ye University of Amsterdam


Local Transport in Gothenburg

Tickets for the tram can be bought with a credit card in yellowish shops called "Pressbyrån", sometimes also at "7-eleven".
There is a good app "Västtrafik Togo", which might work with a credit card.
If it doesn't work with your credit card, you can still use it for planning and real time information.

Paying in Sweden

The currency is SEK and not EUR. It is advisable to have a credit card to pay in Sweden and you should know your PIN. German EC-Cards with V-Pay are also known to work.

Travelling to Gothenburg

If you come from a member state of the EU, your national identity card is enough to enter the country - make sure it is not out of date, it might be checked, even if you travel to Sweden by train or bus.


There are ships from and to Germany and Denmark (Fredrikshavn).



Gothenburg has an international Airport, Landvetter/GOT. Gothenburg is about 4h by train from Stockholm and Copenhagen (which have bigger airports). From the airport, you can use the bus, and choose anything of the suggestions on the right, to end up in the city (the last option is the main train station):

Enivronmental impact

Apart from the obvious, it is unlcear how to rank the ships/ferries. According to some sources, they are worse than flying, if you split emissions by money spent and use an (expensive) overnight ship.