Infinitely generated symbolic Rees algebras over finite fields

2017/03/31 by Akiyoshi Sannai, Hiromu Tanaka
Computer Science · Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Field (mathematics) #Finitely-generated abelian group #Ideal (ethics) #Polynomial and algebraic computation #Polynomial ring #Prime (order theory) #Prime ideal #math.AC #math.AG

paper · pdf · doi:10.2140/ant.2019.13.1879

published as Alg. Number Th. 13 (2019) 1879-1891 · 16 pages, v2: minor revisions, v3: minor revisions

openalex created_date 2017/05/05 · arxiv created 2019/06/14 · openalex publication_date 2019/10/09 · arxiv updated 2019/10/16 · openalex updated_date 2026/08/05

Abstract

For the polynomial ring over an arbitrary field with twelve variables, there exists a prime ideal whose symbolic Rees algebra is not finitely generated.

Citations

• Hilbert’s 14th problem over finite fields and a conjecture on the cone of curves
• Algebraic Geometry