Periodic phenomena in stable motivic homotopy theory

Jackson Morris

Periodic phenomena in stable motivic homotopy theory

Algebraic Topology 2026-07-20 v1 Algebraic Geometry

Authors: Jackson Morris

Abstract

In this survey, we study how tools from stable homotopy theory have manifested and impacted motivic homotopy theory. In particular, we discuss various motivic Adams spectral sequences, periodicity in the motivic stable homotopy groups of spheres, and synthetic spectra. We conclude with many problems for future investigation.

Keywords

motivic homotopy theory Adams spectral sequences periodicity synthetic spectra stable homotopy groups

Cite

@article{arxiv.2607.18165,
  title  = {Periodic phenomena in stable motivic homotopy theory},
  author = {Jackson Morris},
  journal= {arXiv preprint arXiv:2607.18165},
  year   = {2026}
}

Comments

40 page, 1 figure. Contributed survey for AMS Contemporary conference proceedings for Fall 2025 Midwest Topology Seminar "Equivariant, Motivic, and Physical Topology in the Midwest". Comments welcome!