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arXiv · 2605.22494

Divisibility phenomena in motivic Bloch--Ogus theory

Jean-Louis Colliot-Thélène·Stefan Schreieder
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Abstract

Let X be a smooth projective variety over a field k. For k separably closed, we prove that the subgroup of unramified classes in the Milnor K-group $K^M_i(k(X))$ of the function field of X is contained in the subgroup of n-divisible elements of $K^M_i(k(X))$ for any integer n invertible in k. This generalizes to a statement for unramified motivic cohomology of arbitrary bidegree. We further show that whenever k is finite or separably closed and l is a prime invertible in k, then all but the last step in the Bloch--Ogus filtration of the motivic cohomology of X are l-divisible up to torsion. Generalizations of this last result to arbitrary quasi-projective k-schemes are also proven.

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Jean-Louis Colliot-Thélène, Stefan Schreieder. 2026-05-21. Divisibility phenomena in motivic Bloch--Ogus theory. https://arxiv.org/abs/2605.22494

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