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Suslin's singular homology and cohomology

2009/12/07 by Thomas Geisser, Geisser, Thomas H.
Mathematics · #14C25 #14F35 #14F42 #19E15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.0912.1168

openalex publication_date 2009/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss Suslin's singular homology and cohomology. In the first half we examine the p-part in characteristic p, and the situation over non-algebraically closed fields. In the second half we focus on finite base fields. We study finite generation properties, and give a modified definition which behaves like a homology theory: in degree zero it is a copy of Z for each connected component, in degree one it is related to the abelianized (tame) fundamental group, even for singular schemes, and it is expected to be finitely generated in general.

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