Coalgebraic formal curve spectra and spectral jet spaces

Peterson, Eric

doi:10.2140/gt.2020.24.1

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Coalgebraic formal curve spectra and spectral jet spaces

Eric Peterson

Geometry & Topology 24 (2020) 1–47

DOI: 10.2140/gt.2020.24.1

Abstract

We import into homotopy theory the algebrogeometric construction of the cotangent space of a geometric point on a scheme. Specializing to the category of spectra local to a Morava $K$ –theory of height $d$ , we show that this can be used to produce a choice-free model of the determinantal sphere as well as an efficient Picard-graded cellular decomposition of $K (ℤ_{p}, d + 1)$ . Coupling these ideas to work of Westerland, we give a “Snaith’s theorem” for the Iwasawa extension of the $K (d)$ –local sphere.

Keywords

chromatic homotopy, formal group, Morava $E$–theory, determinantal sphere, inverse limit, comodule

Mathematical Subject Classification 2010

Primary: 55N22

Secondary: 55P20, 55P60

References

Publication

Received: 29 June 2017

Revised: 8 June 2019

Accepted: 13 July 2019

Published: 25 March 2020

Proposed: Mark Behrens

Seconded: Stefan Schwede, Haynes R Miller

Authors

Eric Peterson
Department of Mathematics Harvard University Cambridge, MA United States
http://chromotopy.org

Volume 24, issue 1 (2020)