\'Etale motives of geometric origin
Algebraic Geometry
2024-06-21 v2
Abstract
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.
Cite
@article{arxiv.2405.07095,
title = {\'Etale motives of geometric origin},
author = {Raphaël Ruimy and Swann Tubach},
journal= {arXiv preprint arXiv:2405.07095},
year = {2024}
}
Comments
Reorganisation of the proof of the main theorem, the ring of coefficients now has to be ind-regular. 14 pages, comments welcome!