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arXiv · 1404.4349

Refinements to patching and applications to field invariants

David Harbater·Julia Hartmann·Daniel Krashen
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Abstract

We introduce a notion of refinements in the context of patching, in order to obtain new results about local-global principles and field invariants in the context of quadratic forms and central simple algebras. The fields we consider are finite extensions of the fraction fields of two-dimensional complete domains that need not be local. Our results in particular give the u-invariant and period-index bound for these fields, as consequences of more general abstract results.

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David Harbater, Julia Hartmann, Daniel Krashen. 2014-04-16. Refinements to patching and applications to field invariants. https://doi.org/10.1093/imrn%2Frnu278

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