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Results tagged with homotopy-theory
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user 13647
Homotopy theory is an important sub-field of algebraic topology. It is mainly concerned with the properties and structures of spaces which are invariant under homotopy. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces.
11
votes
1
answer
589
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Model category structures on dga's in a ringed topos
In the introduction to his paper "Towards a non-abelian $p$-adic Hodge theory", Olsson says that for any ringed topos $(\mathcal{T},\mathcal{O})$ with $\mathcal{O}$ a sheaf of $\mathbb{Q}$-algebras, t …
- 1,838
11
votes
1
answer
671
views
Pro-algebraic versus continuous Galois cohomology, and schematic homotopy types
I've been thinking about Bertrand Toen's approach to studying the homotopy theory of schemes, and I've come across an inconsistency in my understanding of the subject that I was hoping somebody might …
- 1,838
7
votes
1
answer
301
views
Mapping spaces in complete Segal spaces and quasi-categories
Complete Segal spaces and quasi-categories are two common models for the theory of $(\infty,1)$-categories, and both are equipped with a natural notion of hom spaces. For complete Segal spaces, which …
- 1,838
2
votes
Accepted
Pro-algebraic versus continuous Galois cohomology, and schematic homotopy types
This answer is due to Jon Pridham.
While we might not expect $H^i(G_k,V)=H^i(G_k^\mathrm{alg},V)$ for every finite dimensional, continuous $G_k$-representation $V$, there are certain results from the …
- 1,838