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arXiv · 2608.08012

Invariance of Grothendieck-Witt groups under subintegral extensions and cancellation of quadratic spaces

Jebasingh R
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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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Jebasingh R. 2026-08-08. Invariance of Grothendieck-Witt groups under subintegral extensions and cancellation of quadratic spaces. https://arxiv.org/abs/2608.08012

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