ALGEBRAICπ2(S2)

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ABSTRACT For the algebraic sphere S2 defined as the zero set of the equation x2 1 + x2 2 + x2 3 = 1 in C3, we see that there are polynomial maps fn: S2 → S2 of each degree. For the algebraic sphere S2 defined as the suspension of S1 = C-(0) in the category AFFC of based affine schemes of countable type over C, the set HomAFFC(S2, S2) modulo homotopy is seen, using standard definitions adapted to our algebraic situation, to be (ZxZ)/ψ where ψ collapses (Zx0) ∪ (0xZ) to a point.