The concept of a simple point of an abstract algebraic variety

1947/01/01 by Oscar Zariski · 87 citations
Computer Science · Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic number #Algebraic variety #Epistemology #Geometry #Mathematical analysis #Mathematics #Point (geometry) #Polynomial and algebraic computation #Pure mathematics #Simple (philosophy) #Singular point of an algebraic variety #Statistics #Variety (cybernetics)

paper · doi:10.1090/s0002-9947-1947-0021694-1

published in Transactions of the American Mathematical Society 62(1), 1-52 (American Mathematical Society)

openalex publication_date 1947/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/03/11

Abstract

simple loci.39 10.1.Algebraic ground field extensions.39 10.2.Jacobian criterion for absolutely simple loci.41 11.Intrinsic characterizations of absolutely simple loci.43 11.1.Differential characterization.43 11.2.Direct verification of the local character of the definition.44 11.3.André Weil's criterion.

Citations

• On the structure and ideal theory of complete local rings
• Beitr�ge zur Arithmetik kommutativer Integrit�tsbereiche
• On the Structure and Ideal Theory of Complete Local Rings
• Prime ideals and integral dependence
• Some Results in the Arithmetic Theory of Algebraic Varieties

Cited by

• The Geometry of Schemes
• Desingularization of Two-Dimensional Schemes
• The Hironaka theorem on resolution of singularities (Or: A proof we always wanted to understand)
• Regular local ring [wikipedia]
• Zariski tangent space [wikipedia]