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WebApr 24, 2012 · 2010 Mathematics Subject Classification: Primary: 14Cxx Secondary: 14G10 18F25 [][] $ \newcommand{\CH}{\mathrm{CH}} $ The Chow ring of a non-singular quasi-projective algebraic variety is the ring of rational equivalence classes of algebraic cycles (cf. Algebraic cycle) on that variety.Multiplication in this ring is defined in terms of … WebChow Group Problem: If A is a regular local ring, then CHi(A) = 0 for i 6= d, and CHd(A) ∼= Z (where the generator is [A]). Interlude on Divisor Class Groups In fact, when A is an … WebLet z i ( X, m) be the free abelian group generated by all codimension i subvarieties on X × Δ m which intersect all faces X × Δ j properly for all j < m. Then, for each i, these groups assemble to give, with the restriction maps to these faces, a simplicial group whose homotopy groups are the higher Chow groups CH^i (X,m) (m=0 gives the ... nature\u0027s way the song