Families of zero cycles and divided powers: I. Representability

2008/03/05 by Rydh, David
#14C05 #14C25 #14L30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0803.0618

Abstract

For any separated algebraic space X/S we construct a separated algebraic space Γ^d(X/S) -- the space of divided powers -- which parameterizes zero cycles of degree d on X. The space of divided powers for an affine scheme is given by the spectrum of the algebra of divided powers. In characteristic zero or when X/S is flat, the constructed space coincides with the symmetric product Sym^d(X/S). We also prove several fundamental results on the kernels of multiplicative polynomial laws necessary for the construction of Γ^d(X/S).

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