PreprintCC BY 4.0HAL
Flasque resolutions of linear reductive group schemes
Abstract
This paper studies flasque resolutions for linear reductive group schemes over arbitrary bases, extending Colliot-Thélène's theory. A flasque resolution exists for any linear reductive group scheme over a connected base scheme (resp. a quasi-compact, quasi-separated base scheme). The construction relies on Borovoi's fundamental group and descent theory involving automorphisms of Chevalley groups. Applications include R-equivalence for reductive group schemes over rings and over a field of cohomological dimension at most 2.
Related
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- A Calabi--Matsushima decomposition for real reductive group actions
BibTeX
@misc{gille2026flasque,
title = {{Flasque resolutions of linear reductive group schemes}},
author = {Philippe Gille},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2610.03781},
eprint = {2610.03781},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05770864v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Flasque resolutions of linear reductive group schemes
AU - Philippe Gille
PY - 2026
DA - 2026/09/30
PB - HAL
DO - 10.48550/arxiv.2610.03781
UR - https://hal.science/hal-05770864v1
AB - This paper studies flasque resolutions for linear reductive group schemes over arbitrary bases, extending Colliot-Thélène's theory. A flasque resolution exists for any linear reductive group scheme over a connected base scheme (resp. a quasi-compact, quasi-separated base scheme). The construction relies on Borovoi's fundamental group and descent theory involving automorphisms of Chevalley groups. Applications include R-equivalence for reductive group schemes over rings and over a field of cohomological dimension at most 2.
ER -