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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(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