Birational localization of motivic spaces over perfect fields is equivalent to S^{2,1}-nullification, making π0^{b A^1} a birational invariant for proper schemes.
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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.
citing papers explorer
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Birational Algebraic Topology
Birational localization of motivic spaces over perfect fields is equivalent to S^{2,1}-nullification, making π0^{b A^1} a birational invariant for proper schemes.
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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.
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Shape theory for condensed anima
Shape theory for condensed anima recovers classical shape for paracompact compactly generated and locally contractible spaces while extending sheaf-condensed cohomology comparisons.