nLab spectral affine line



Higher geometry

Higher algebra

Arithmetic geometry



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.


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 21:00:48. See the history of this page for a list of all contributions to it.