nLab
spectral affine line

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Contents

Idea

The concept of spectral affine line is the generalization of the concept of affine line to spectral geometry, in the sense of E-∞ geometry.

Given a (connective) E-∞ ring RR, then the spectral affine line over RR is the affine spectral scheme given by the spectral symmetric algebra on a single generator:

𝔸 R 1=Spec(Sym R(R)). \mathbb{A}^1_R = Spec( Sym_R(R) ) \,.

(e.g. Lurie Schemes, below prop. 2.20)

For R=𝕊R = \mathbb{S} the sphere spectrum, then this may be called the absolute spectral affine line. This is discussed in Strickland-Turner 97.

References

Some general comments are in

The absolute spectral affine line over R=𝕊 R = \mathbb{S} the sphere spectrum is discussed in

Created on March 19, 2017 at 17:00:48. See the history of this page for a list of all contributions to it.