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arXiv · 1904.10849

Coalgebraic Formal Curve Spectra and the Annular Tower

Eric C. Peterson
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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.

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Eric C. Peterson. 2019-04-24. Coalgebraic Formal Curve Spectra and the Annular Tower. https://doi.org/10.2140/gt.2020.24.1

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