3 papers
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.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.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…