A survey on algebraic dilatations

2023/06/29 by Adrien Dubouloz, Arnaud Mayeux, Dubouloz, Adrien +3
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2306.17003

openalex publication_date 2023/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and theoretical aspects and the other applications to existing theories.

Citations

• Quelques remarques sur la notion de modification affine
• Affine modifications and affine hypersurfaces with a very transitive automorphism group
• Comparing Bushnell-Kutzko and Sécherre's constructions of types for GL_N and its inner forms with Yu's construction

Related

• Multi-centered dilatations, congruent isomorphisms and Rost double deformation space
• A caricature of dilation theory
• Dilation theory: a guided tour
• Exercises in the birational geometry of algebraic varieties
• Ando dilations and inequalities on noncommutative domains