Normalized Berkovich spaces and surface singularities

  title={Normalized Berkovich spaces and surface singularities},
  author={Lorenzo Fantini},
  journal={arXiv: Algebraic Geometry},
We define normalized versions of Berkovich spaces over a trivially valued field $k$, obtained as quotients by the action of $\mathbb R_{>0}$ defined by rescaling semivaluations. We associate such a normalized space to any special formal $k$-scheme and prove an analogue of Raynaud's theorem, characterizing categorically the spaces obtained in this way. This construction yields a locally ringed $G$-topological space, which we prove to be locally isomorphic to a Berkovich space over the field $k… Expand
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