higher geometry / derived geometry
geometric little (∞,1)-toposes
geometric big (∞,1)-toposes
function algebras on ∞-stacks?
derived smooth geometry
symmetric monoidal (∞,1)-category of spectra
transfinite arithmetic, cardinal arithmetic, ordinal arithmetic
prime field, p-adic integer, p-adic rational number, p-adic complex number
arithmetic geometry, function field analogy
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:
(e.g. Lurie Schemes, below prop. 2.20)
For $R = \mathbb{S}$ 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 $R = \mathbb{S}$ 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.