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Invariance of Grothendieck-Witt groups under subintegral extensions and cancellation of quadratic spaces
Jebasingh R
https://arxiv.org/abs/2608.08012 https://arxiv.org/pdf/2608.08012 https://arxiv.org/html/2608.08012
arXiv:2608.08012v1 Announce Type: new
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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