# Normalized Berkovich spaces and surface singularities

```@article{Fantini2014NormalizedBS,
title={Normalized Berkovich spaces and surface singularities},
author={Lorenzo Fantini},
journal={arXiv: Algebraic Geometry},
year={2014}
}```
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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