Arc-descent conjecture for rational motivic cohomology presheaves

For an algebraic space XX, let \Cmot(X;\Q(r)):=Γ(X;\Q(r))\Cmot(X; \Q(r)):=\Gamma(X;\Q(r)) denote the rational motivic cohomology spectrum with Tate twist rr. For every integer rZr\in\Z, consider the presheaf X\Cmot(X;\Q(r))X\mapsto \Cmot(X;\Q(r)). Arc-descent conjecture. For every integer rZr\in\Z, the presheaf \Cmot(;\Q(r))\Cmot(-;\Q(r)) satisfies arc-descent. This predicts a stronger form of descent than the established hh-descent for rational motives; the preceding discussion presents it as more credible than arc-descent for the full presheaf \DM\Q\DM_\Q^*, but the conjecture's resolution is not specified here.

Sources & referencesView supporting material

Primary source

Adeel A. Khan, “Descendability and descent in topological weaves”, arXiv:2607.07137 (2026).

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