nLab synthetic algebraic geometry

Idea

synthetic$\;$ algebraic geometry

Related concepts

• algebraic geometry

• synthetic mathematics

  • synthetic geometry

  • synthetic topology

  • synthetic differential geometry

  • synthetic differential topology

  • synthetic homotopy theory

  • synthetic $(\infty,1)$-category theory

  • synthetic probability theory

References

• Anders Kock, §I.12 in: Synthetic Differential Geometry, Cambridge University Press (1981, 2006) [pdf, doi:10.1017/CBO9780511550812]

• Ingo Blechschmidt, Using the internal language of toposes in algebraic geometry, PhD thesis (2017) [pdf, pdf]

• Felix Cherubini, Thierry Coquand, Matthias Hutzler: A foundation for synthetic algebraic geometry, Mathematical Structures in Computer Science 34 Special Issue 9: Advances in Homotopy type theory (2024) 1008-1053 [doi:10.1017/S0960129524000239, arXiv:2307.00073]

• Felix Cherubini, A Foundation for Synthetic Algebraic Geometry, talk at Homotopy Type Theory Electronic Seminar Talks (Oct 2023) [slides:pdf, video:YT]

• Synthetic Algebraic Geometry in the Zariski-Topos (Github)

On projective spaces:

• Felix Cherubini, Thierry Coquand, Matthias Hutzler, David Wärn: Projective Space in Synthetic Algebraic Geometry, 2024, [arxiv:2405.13916]

On Châtelet’s theorem:

• Thierry Coquand, Hugo Moeneclaey, Chatelet’s Theorem in Synthetic Algebraic Geometry [arXiv:2504.08326]