Coalgebraic Formal Curve Spectra and the Annular Tower

Abstract

We import into homotopy theory the algebro-geometric 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 $K({\mathbb{Z}}_p,d+1)$. Coupling these ideas to work of Westerland, we give a "Snaith's theorem" for the Iwasawa extension of the $K(d)$-local sphere.

Submitted as author's 2015 PhD thesis, submitted for journal publication in 2017, only realized in 2019 that it wasn't available on the arXiv

References in corpus (1)

• The higher Morita category of $E_n$-algebras

Cited by in corpus (2)

• Morava K-theory and Filtrations by Powers
• Wilson Spaces, Snaith Constructions, and Elliptic Orientations