Workshop on Synthetic Algebraic Geometry

University of Augsburg
October 2-6, 2023

Other SAG meetings


Synthetic algebraic geometry (SAG), is the study of algebraic geometry by synthetic means - instead of building up everything from ZF(C), we reason internal to a topos whose internal sets already contain the objects of interest. Our topos is called the (higher) Zariski topos and is given by Zariski-sheaves on affine schemes of finite type over an arbitrary base ring. Higher sheaves are neccessary to interpret the homotopy type theory we use to have, in addition to the usual convenience, an easy access to cohomology groups.
We have also begun to explore 𝔸¹-homotopy theory and algebraic stacks. The foundation is described here and more drafts can be found here.


All talks are in Building L (map below), room 2004. Coffee breaks will be in 2006.
The links below lead to videos hosted on this server, there is also a playlist on youtube.

Time Mon Tue Wed Thu Fri
9:30 - 10:30 Overview Excursion Cohomology I Blow ups Serre Affineness
11:00 - 12:00 HoTT+Modalities Excursion Smoothness I Smoothness II Stacks
14:00 - 15:00 Introduction to SAG Excursion Specific SAG Stacks and 1-definite description Cohomology I.5
15:30 - 16:30 Constructive Equivalence of Functor of Points… Excursion Models A1-homotopy theory 2-Cats and Cosheaves

Note that the excursion starts at 6:32am at the train station.


Here are some rough notes, who gave talks on which topic:

Speaker Topic
Max Zeuner Constructive Equivalence of Functor of Points and Topological Approach
Hugo Moeneclaey Smooth Schemes, Stacks, A1-homotopy theory
Felix Cherubini History and Overview, Cohomology, A1-homotopy theory
Lukas Stoll Modalities
Nicolas Beck Stacks and 1-definite description
Matthias Hutzler Introduction to Schemes, Models
Marc Nieper-Wißkirchen Blow ups (classically)
Ingo Blechschmidt Towards Specific Synthetic Algebraic Geometry, Serre Affineness
Ilia Pirashvili 2-Categories, Connected Components and fundamental groupoids as cosheaves
Peter Arndt Traditional A1-homotopy theory


Ingo Blechschmidt University of Augsburg
Fabian Endres University of Augsburg
Matthias Hutzler University of Gothenburg
Felix Cherubini University of Gothenburg
Marc Nieper-Wißkirchen University of Augsburg
Lukas Stoll University of Augsburg
Hugo Moeneclaey University of Gothenburg
Max Zeuner University of Stockholm
Nicolas Beck Freie Universität Berlin
Heiko Braun University of Bonn
Tim Lichtnau University of Bonn
Peter Arndt (joining on Oct 3rd) University of Düsseldorf
Ilia Pirashvili University of Augsburg


Local transportation and points of interest

First of all: Google maps does not work for public transport in Augsburg.
You can use this page, to figure out how to use public transport.

You can take tram 3 to get from the train station to campus.
The workshop is in the building L (L1 on the map):

The workshop dinner will be at the Indian restaurant Sangam:


Register via email to Carolina Dujo ( Let her know if you need a hotel room or financial support.

Financial support

If you need financial support to join the meeting, write an informal email to Marc Nieper-Wißkirchen to let us know.