The Galois groupoid of G-spectra is equivalent to the étale fundamental groupoid of the Burnside ring of G.
Integral Transforms and Drinfeld Centers in Derived Algebraic Geometry
5 Pith papers cite this work. Polarity classification is still indexing.
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The condensed fundamental group of Spec(Z) is non-trivial, hence Spec(Z) is not condensed contractible.
Provides spectral description of central torus convolution actions and shows the ℓ-adic categorical Langlands conjecture passes to quotients by central tori in char 0 and for Langlands-Shahidi parameters in all char, extending to PGL_n.
Models Rozansky-Witten theory of T*X via sheaves of categories from Perf(X×A¹), constructing hybrid Lagrangian objects whose Homs are matrix factorizations.
Shape theory for condensed anima recovers classical shape for paracompact compactly generated and locally contractible spaces while extending sheaf-condensed cohomology comparisons.
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On Galois categories and condensed contractible schemes
The condensed fundamental group of Spec(Z) is non-trivial, hence Spec(Z) is not condensed contractible.