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Journal Article

Coalgebraic formal curve spectra and spectral jet spaces

MPS-Authors
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Peterson,  Eric
Max Planck Institute for Mathematics, Max Planck Society;

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http://dx.doi.org/10.2140/gt.2020.24.1
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Citation

Peterson, E. (2020). Coalgebraic formal curve spectra and spectral jet spaces. Geometry & Topology, 24(1), 1-47. doi:10.2140/gt.2020.24.1.


Cite as: https://hdl.handle.net/21.11116/0000-0007-FE2C-B
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.Zp; d C1/. Coupling these ideas to work of Westerland,
we give a “Snaith’s theorem” for the Iwasawa extension of the K.d/–local sphere.