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arXiv · 1501.07631

Milnor-Witt $K$-groups of local rings

Stefan Gille·Stephen Scully·Changlong Zhong
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Abstract

We introduce Milnor-Witt $K$-groups of local rings and show that the $n$th Milnor-Witt $K$-group of a local ring $R$ which contains an infinite field of characteristic not $2$ is the pull-back of the $n$th power of the fundamental ideal in the Witt ring of $R$ and the $n$th Milnor $K$-group of $R$ over the $n$th Milnor $K$-group of $R$ modulo $2$. This generalizes the work of Morel-Hopkins on Milnor-Witt $K$-groups of fields.

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Stefan Gille, Stephen Scully, Changlong Zhong. 2015-05-20. Milnor-Witt $K$-groups of local rings. https://arxiv.org/abs/1501.07631

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