Families of zero cycles and divided powers: I. Representability

Abstract

For any separated algebraic space $X/S$ we construct a separated algebraic space ${\Gamma }^d(X/S)$ -- 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 $Sy{m}^d(X/S)$. We also prove several fundamental results on the kernels of multiplicative polynomial laws necessary for the construction of ${\Gamma }^d(X/S)$.

52 pages

References in corpus (1)

• Revêtements étales et groupe fondamental (SGA 1)