# nLab spectral affine line

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## Examples

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## Higher algebras

• symmetric monoidal (∞,1)-category of spectra

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## Theorems

#### Arithmetic geometry

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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 $R$, then the spectral affine line over $R$ is the affine spectral scheme given by the spectral symmetric algebra on a single generator:

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

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

## References

The absolute spectral affine line over $R = \mathbb{S}$ the sphere spectrum is discussed in
• Neil Strickland, Paul Turner, Rational Morava $E$-theory and $D S^0$, Topology Volume 36, Issue 1, January 1997, Pages 137-151 (pdf)