Projective geometry for blueprints
Javier L\'opez Pe\~na, Oliver Lorscheid

TL;DR
This paper extends the Proj-construction to blue schemes, enabling the definition of projective spaces and varieties over blueprints, and explores their descent to F_1-models with explicit examples like the Grassmannian.
Contribution
It introduces a generalized Proj-construction for blue schemes, allowing projective geometry over blueprints and F_1-models, with explicit case studies.
Findings
Defined projective space and varieties over blueprints.
Demonstrated descent of subvarieties to F_1-models.
Explicit analysis of the Grassmannian Gr(2,4).
Abstract
In this note, we generalize the Proj-construction from usual schemes to blue schemes. This yields the definition of projective space and projective varieties over a blueprint. In particular, it is possible to descend closed subvarieties of a projective space to a canonical F_1-model. We discuss this explicitly in case of the Grassmannian Gr(2,4).
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
