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\'Etale motives of geometric origin

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arxiv 2405.07095 v2 pith:7RTNOSV7 submitted 2024-05-11 math.AG

Raphaël Ruimy , Swann Tubach This is my paper · ORCID
classification math.AG
keywords etalemotivesgeometricoriginpropertyaffordanswerback
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Over qcqs finite-dimensional schemes, we prove that \'etale motives of geometric origin can be characterised by a constructibility property which is purely categorical, giving a full answer to the question "Do all constructible \'etale motives come from geometry?" which dates back to Cisinski and D\'eglise's work. We also show that they afford the continuity property and satisfy h-descent and Milnor excision.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Descendability and descent in topological weaves

    math.AG 2026-07 accept novelty 7.0 of 10

    Finitely presented surjections of algebraic spaces are descendable in topological weaves, yielding v-descent for rational motivic sheaves and h-descent for étale motivic spectra under bounded cohomological dimension.

  2. Deligne 1-motives with torsion and \'etale motives

    math.AG 2025-06 conditional novelty 7.0 of 10

    For Q-schemes and Dedekind schemes, the motivic t-structure exists on 1-motives with integral coefficients, with heart the abelian category of Deligne 1-motives with torsion.

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