[Sur le type d'homéomorphisme des espaces de valuations]
Soit X une variété algébrique définie sur un corps algébriquement clos. On étudie la fibre de l'espace de Riemann–Zariski au-dessus d'un point fermé . Si x est régulier, on démontre que son type d'homéomorphisme ne dépend que de la dimension de X. Si x est un point singulier d'une surface normale, on démontre qu'il ne dépend que de la classe du graphe d'une bonne résolution de modulo une relation d'équivalence précise. Ces deux résultats sont aussi vrais pour l'entrelac non archimédien normalisé de x dans X.
Let X be an algebraic variety defined over an algebraically closed field. We study the fiber of the Riemann–Zariski space above a closed point . If x is regular, we prove that its homeomorphism type only depends on the dimension of X. If x is a singular point of a normal surface, we show that it only depends on the dual graph of a good resolution of up to some precise equivalence. Both results also hold for the normalized non-Archimedean link of x in X.
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@article{CRMATH_2015__353_6_541_0,
author = {de Felipe, Ana Bel\'en},
title = {On the homeomorphism type of some spaces of valuations},
journal = {Comptes Rendus. Math\'ematique},
pages = {541--544},
publisher = {Elsevier},
volume = {353},
number = {6},
year = {2015},
doi = {10.1016/j.crma.2015.03.015},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2015.03.015/}
}
TY - JOUR AU - de Felipe, Ana Belén TI - On the homeomorphism type of some spaces of valuations JO - Comptes Rendus. Mathématique PY - 2015 SP - 541 EP - 544 VL - 353 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.03.015/ DO - 10.1016/j.crma.2015.03.015 LA - en ID - CRMATH_2015__353_6_541_0 ER -
%0 Journal Article %A de Felipe, Ana Belén %T On the homeomorphism type of some spaces of valuations %J Comptes Rendus. Mathématique %D 2015 %P 541-544 %V 353 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.03.015/ %R 10.1016/j.crma.2015.03.015 %G en %F CRMATH_2015__353_6_541_0
de Felipe, Ana Belén. On the homeomorphism type of some spaces of valuations. Comptes Rendus. Mathématique, Tome 353 (2015) no. 6, pp. 541-544. doi : 10.1016/j.crma.2015.03.015. http://www.numdam.org/articles/10.1016/j.crma.2015.03.015/
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