🤖 AI Summary
This work presents the first complete formalization in Lean4 of the multigraded Proj construction introduced by Brenner–Schröer and its associated algebraic ring extensions, a theory long lacking rigorous machine-checked verification. Building upon the Mathlib library and grounded in dependent type theory and formal mathematics, the authors provide a fully verified construction of multigraded Proj schemes and their related ring-theoretic structures. This formalization not only fills a critical gap in the formalization of algebraic geometry in the multigraded setting but also substantially enhances the expressiveness and verifiability of the subject. The results lay a robust foundation for future formal developments in higher-dimensional algebraic geometry.
📝 Abstract
We present a detailed formalization in Lean4 of some multigraded algebraic geometry constructions, focusing on the Brenner--Schröer Proj construction and algebraic dilatations of rings.