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Results tagged with stable-homotopy
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user 2503
Stable homotopy theory is that part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor.
7
votes
Morphisms of $\mathbb E_l$-rings between $\mathbb E_k$-rings for $l<k$
Let $R$ be an $E_\infty$-ring spectrum and write $R\{t\}$ (resp. $R[t]$) for the free $E_\infty$-$R$-algebra (resp. free $E_1$-$R$-algebra) on one generator $t$ (in degree zero). This notation is com …
- 5,901
2
votes
Accepted
Integral transform on noncommutative spaces
Let $DGCat_k$ denote the $\infty$-category obtained by localizing the category of dg-categories at Morita equivalences. This is presented by the Morita model structure on the category of dg-categorie …
- 5,901
7
votes
Accepted
When do the polynomial algebra and free algebra coincide in brave new algebra?
Any morphism of $R$-algebras $\varphi : R\{t\} \to R[t]$ is determined up to homotopy by an element of $\pi_0(R[t]) \approx \pi_0(R)[t]$. If $\varphi$ is an equivalence, then this element must be the …
- 5,901
23
votes
Accepted
Motivation and potential applications of spectral algebraic geometry
This is not really an answer to your question, just an attempt to address your question from the comments.
There are various flavours of homotopical or higher algebraic geometry that are commonly con …
- 5,901