Motivic colimits and extended powers
K-Theory and Homology
2022-07-12 v2 Algebraic Geometry
Algebraic Topology
Category Theory
Abstract
We define a notion of colimit for diagrams in a motivic category indexed by a presheaf of spaces (e.g. an \'etale classifying space), and we study basic properties of this construction. As a case study, we construct the motivic analogs of the classical extended and generalized powers, which refine the categorical versions of these constructions as special cases. We also offer more computationally tractable models of these constructions using equivariant motivic homotopy theory. This is the first in a series of papers on power operations in motivic stable homotopy theory.
Keywords
Cite
@article{arxiv.2104.01057,
title = {Motivic colimits and extended powers},
author = {Tom Bachmann and Elden Elmanto and Jeremiah Heller},
journal= {arXiv preprint arXiv:2104.01057},
year = {2022}
}
Comments
32 pages, comments welcome, first of a series on motivic power operations