3 papers
math.AG2025
Chatelet's Theorem in Synthetic Algebraic Geometry
Thierry Coquand, Hugo Moeneclaey
We prove a version of Chatelet's Theorem about Severi-Brauer variety having rational points in the setting of synthetic algebraic geometry. We work over an arbitrary base ring.
math.AG2025
Differential Geometry of Synthetic Schemes
Felix Cherubini, Matthias Hutzler, Hugo Moeneclaey +1
Synthetic algebraic geometry uses homotopy type theory extended with three axioms to develop algebraic geometry internal to a higher version of the Zariski topos. In this article w…
math.LO2024
A Foundation for Synthetic Stone Duality
Felix Cherubini, Thierry Coquand, Freek Geerligs +1
The language of homotopy type theory has proved to be appropriate as an internal language for various higher toposes, for example with Synthetic Algebraic Geometry for the Zariski…