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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.