Singular Homology of Arithmetic Schemes

2007/03/28 by Alexander Schmidt, Schmidt, Alexander · 1 citation
Computer Science · Mathematics · #11R37 #19E15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.math/0703853

openalex publication_date 2007/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a singular homology theory on the category of schemes of finite type over a Dedekind domain and verify several basic properties. For arithmetic schemes we construct a reciprocity isomorphism between the integral singular homology in degree zero and the abelianized modified tame fundamental group.

Cited by

• Zero-cycles on quasi-projective surfaces over p-adic fields

Related

• Suslin's singular homology and cohomology
• Tame Class Field Theory for Singular Varieties over Algebraically Closed Fields
• Arithmetic homology and an integral version of Katos conjecture
• Tame coverings of arithmetic schemes
• Relative K-theory and class field theory for arithmetic surfaces