On the splitting principle for cohomological invariants of reflection groups

Stefan Gille; Christian Hirsch

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arXiv · 1908.08146

On the splitting principle for cohomological invariants of reflection groups

Stefan Gille·Christian Hirsch

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Abstract

Let $\mathrm{k}_{0}$ be a field and $W$ a finite orthogonal reflection group over $\mathrm{k}_{0}$. We prove Serre's splitting principle for cohomological invariants of $W$ with values in Rost's cycle modules (over $\mathrm{k}_{0}$) if the characteristic of $\mathrm{k}_{0}$ is coprime to $|W|$. We then show that this principle for such groups holds also for Witt- and Milnor-Witt $K$-theory invariants.

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Stefan Gille, Christian Hirsch. 2019-08-21. On the splitting principle for cohomological invariants of reflection groups. https://arxiv.org/abs/1908.08146

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