What $Ell$ sees that $K$ doesn't (when $p >3$)
Algebraic Topology
2020-07-07 v2 Number Theory
Abstract
We use Andrew Baker's analysis of the cofiber of the endomorphism of the -adic elliptic spectrum () defined by multiplication by the `Hasse invariant' to present its completion away from the locus of ordinary elliptic curves as a sum of roughly copies (indexed by supesingular elliptic curves) of -adic lifts of the height two mod cohomology theory . See a recent paper of Zhu Yifei for a much deeper exploration of the topics considered in this note.
Cite
@article{arxiv.2006.16093,
title = {What $Ell$ sees that $K$ doesn't (when $p >3$)},
author = {Jack Morava},
journal= {arXiv preprint arXiv:2006.16093},
year = {2020}
}
Comments
A spin-off from the May 2020 Perimeter Institute conference on elliptic cohomology and physics. Thanks to the conference organizers, and especially to Andrew Baker, Nitu Kitchloo, and Ken Ono for conversations and help with this note