2025/10/23 by Allen, Keita, Piessevaux, Lucas
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2510.20197
We prove a topological reconstruction result for the category of cellular A-equivariant motivic spectra over the complex numbers where A is a finite abelian group: after completion at an arbitrary prime, this is equivalent to the completion of a category of synthetic A-equivariant spectra. The latter is a deformation of equivariant spectra which categorifies the equivariant perfect even filtration and is closely related to the equivariant Adams--Novikov spectral sequence. Our main computational input is a description of the bigraded homotopy groups of equivariant algebraic cobordism in terms of equivariant formal group laws.