| Résume | I will be speaking of local-global principles obtained by working on non-Archimedean Berkovich analytic curves, which are defined over complete rank 1 valued fields. By local considerations in the case of quadratic forms, one can then obtain upper bounds on a related invariant. I will also speak of some recent generalizations obtained through this approach together with K.J. Becher and N. Daans, which make it possible to get rid of the "rank 1" assumption on the valuation.
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