Uniform Rost nilpotence and birational motives
Abstract
For a field extension E/k and a Chow motive M, let IE(M)=ker(Endk(M)⟶ EndE(ME)) be the base-change ideal. We establish explicit nilpotence bounds for these ideals in several geometric settings. We also prove effective generic descent: if M is a summand of h(X)(a) and Mk(X) has uniform Rost exponent s, then M has exponent s(dim X+1). This yields the integral exponent 2n−1 for twisted Milnor hyperplane sections of dimension 2n−2. In characteristic zero, a weighted local-block refinement of the multilinear Rost filtration improves the uniform bounds of Gille and upgrades the elementwise estimates of Rosenschon--Sawant to uniform bounds at the ideal level. Using the Kahn--Sujatha description of pure birational motives, we obtain quantitative lifting results from birational to ordinary Chow motives, with applications to threefolds, including varieties birational to toric models and varieties admitting a decomposition of the diagonal supported on a surface. Finally, we extend the Kok--Zhou detector from individual correspondences to entire base-change ideals, obtaining an explicit ideal nilpotence bound from uniform annihilation of the critical refined unramified cohomology groups.
Related
- F-nilpotence and Hodge filtrations beyond isolated singularities
- Solvability and nilpotence of ind-groups via tangent curves
- Solvability and nilpotence of ind-groups via tangent curves
- Nilpotent Lie algebras of nilpotence class at most three via graphs
- Surjective maps preserving quasi-nilpotence of products of operators
BibTeX
@misc{kumallagov2026uniform,
title = {{Uniform Rost nilpotence and birational motives}},
author = {David Kumallagov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20228},
eprint = {2609.20228},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20228},
}
RIS
TY - UNPB
TI - Uniform Rost nilpotence and birational motives
AU - David Kumallagov
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.20228
UR - https://arxiv.org/abs/2609.20228
AB - For a field extension E/k and a Chow motive M, let I_E(M)=ker(End_k(M)⟶ End_E(M_E)) be the base-change ideal. We establish explicit nilpotence bounds for these ideals in several geometric settings. We also prove effective generic descent: if M is a summand of h(X)(a) and M_k(X) has uniform Rost exponent s, then M has exponent s(dim X+1). This yields the integral exponent 2n−1 for twisted Milnor hyperplane sections of dimension 2n−2. In characteristic zero, a weighted local-block refinement of the multilinear Rost filtration improves the uniform bounds of Gille and upgrades the elementwise estimates of Rosenschon--Sawant to uniform bounds at the ideal level. Using the Kahn--Sujatha description of pure birational motives, we obtain quantitative lifting results from birational to ordinary Chow motives, with applications to threefolds, including varieties birational to toric models and varieties admitting a decomposition of the diagonal supported on a surface. Finally, we extend the Kok--Zhou detector from individual correspondences to entire base-change ideals, obtaining an explicit ideal nilpotence bound from uniform annihilation of the critical refined unramified cohomology groups.
ER -