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arXiv · 1711.00341

Patching over Berkovich Curves and Quadratic Forms

Vlerë Mehmeti
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Abstract

We extend field patching to the setting of Berkovich analytic geometry and use it to prove a local-global principle over function fields of analytic curves. We apply this result to quadratic forms, and combine it with sufficient conditions for local isotropy over a Berkovich curve to obtain applications on the u-invariant. The patching method we adapt was introduced by Harbater and Hartmann, and further developed by these two authors and Krashen. This paper generalizes their results on the local-global principle and quadratic forms.

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Vlerë Mehmeti. 2017-11-01. Patching over Berkovich Curves and Quadratic Forms. https://doi.org/10.1112/s0010437x19007632

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