Suslin homology

In mathematics, the Suslin homology is a homology theory attached to algebraic varieties. It was proposed by Suslin in 1987, and developed by Template:Harvs. 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

$H_i(X,A)={\mathrm{Tor}}_i^{\mathbb{Z}}(C,A)$

where C is a free graded abelian group whose degree n part is generated by integral subschemes of ${\mathrm{△}}^n\times X$, where ${\mathrm{△}}^n$ is an n-simplex, that are finite and surjective over ${\mathrm{△}}^n$.

References

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