2024/12/29 by Chirantan Chowdhury, Chowdhury, Chirantan
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #FOS: Mathematics #K-Theory and Homology (math.KT) #Robotic Mechanisms and Dynamics
paper · pdf · doi:10.48550/arxiv.2412.20548
openalex publication_date 2024/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article is the last of the series of articles where we reprove the foundational ideas of abstract six-functor formalisms developed by Liu-Zheng. We prove the theorem of partial adjoints, which is a simplicial technique of encoding various functors altogether by taking adjoints along specific directions. Combined with the ∞-categorical compactification theorem from the previous article, we can construct abstract six-functor formalisms in reasonable geometric setups of our interest. We also reprove the simplified versions of the DESCENT program due to Liu-Zheng, which allows us to extend such formalisms from smaller to larger geometric setups.