#### Volume 24, issue 1 (2020)

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Coalgebraic formal curve spectra and spectral jet spaces

### Eric Peterson

Geometry & Topology 24 (2020) 1–47
##### 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 $K\left({ℤ}_{p},d+1\right)$. Coupling these ideas to work of Westerland, we give a “Snaith’s theorem” for the Iwasawa extension of the $K\left(d\right)$–local sphere.

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##### Keywords
chromatic homotopy, formal group, Morava $E$–theory, determinantal sphere, inverse limit, comodule
##### Mathematical Subject Classification 2010
Primary: 55N22
Secondary: 55P20, 55P60
##### Publication
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