“Suslin homology”的意思、由来-开放百科全书

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Suslin homology

释义

References

In mathematics, the Suslin homology is a homology theory attached to algebraic varieties. It was proposed by Suslin in 1987, and developed by {{harvs|txt|last1=Suslin|last2= Voevodsky|year=1996}}. It is sometimes called singular homology as it is analogous to the singular homology of topological spaces.

By definition, given an abelian group A and a scheme X of finite type over a field k, the theory is given by

where C is a free graded abelian group whose degree n part is generated by integral subschemes of , where is an n-simplex, that are finite and surjective over .

References

{{citation|title=On Suslin's singular homology and cohomology

|first=Thomas |last=Geisser|year=2009|arxiv=0912.1168|bibcode=2009arXiv0912.1168G}}

{{citation|mr=1432056 |last=Levine|first= Marc|title=Homology of algebraic varieties: an introduction to the works of Suslin and Voevodsky|journal=Bull. Amer. Math. Soc. (N.S.) |volume=34 |year=1997|issue= 3|pages= 293–312 |doi=10.1090/s0273-0979-97-00723-4}}
{{citation|mr=1376246

|last=Suslin|first= Andrei|last2= Voevodsky|first2= Vladimir
|title=Singular homology of abstract algebraic varieties
|journal=Invent. Math. |volume=123 |year=1996|issue= 1|pages= 61–94|doi=10.1007/bf01232367|bibcode=1996InMat.123...61S|citeseerx=10.1.1.46.9175}}

1 : Algebraic geometry

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