Program to prove categorical local Langlands conjecture via compatibility hypothesis for GL_n, induction on Levi subgroups for general groups, plus new spectral finiteness, duality, and admissible ind-coherent sheaf results.
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3 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.
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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The categorical local Langlands conjecture
Program to prove categorical local Langlands conjecture via compatibility hypothesis for GL_n, induction on Levi subgroups for general groups, plus new spectral finiteness, duality, and admissible ind-coherent sheaf results.