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Invariance of Grothendieck-Witt groups under subintegral extensions and cancellation of quadratic spaces
Abstract
Motivated by the work of Ischebeck on the behaviour of algebraic K-theoretic functors under subintegral extensions, we investigate the analogous question in Hermitian K-theory. We prove that Grothendieck-Witt groups in degree zero are invariant under subintegral extensions. We also investigate the cancellation problem for quadratic spaces over geometric subrings of polynomial rings and establish a cancellation theorem for quadratic spaces of sufficiently large Witt index.
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BibTeX
@misc{jebasingh2026invariance,
title = {{Invariance of Grothendieck-Witt groups under subintegral extensions and cancellation of quadratic spaces}},
author = {Jebasingh R},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.08012},
eprint = {2608.08012},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.08012},
}
RIS
TY - UNPB
TI - Invariance of Grothendieck-Witt groups under subintegral extensions and cancellation of quadratic spaces
AU - Jebasingh R
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.08012
UR - https://arxiv.org/abs/2608.08012
AB - Motivated by the work of Ischebeck on the behaviour of algebraic K-theoretic functors under subintegral extensions, we investigate the analogous question in Hermitian K-theory. We prove that Grothendieck-Witt groups in degree zero are invariant under subintegral extensions. We also investigate the cancellation problem for quadratic spaces over geometric subrings of polynomial rings and establish a cancellation theorem for quadratic spaces of sufficiently large Witt index.
ER -