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arXiv · 1010.0341

Un th\'eor\`eme de l'application ouverte sur les corps valu\'es alg\'ebriquement clos

Laurent Moret-Bailly
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Abstract

Let K be an algebraically closed valued field, and let f:X--->Y be a universally open morphism of K-schemes of finite type. We show that the induced map on K-rational points is open for the topologies deduced from the absolute value of K. ------ Soit K un corps valu\'e alg\'ebriquement clos, et soit f:X--->Y un morphisme universellement ouvert de K-sch\'emas de type fini. On montre que l'application de X(K) dans Y(K) induite par f est ouverte pour les topologies d\'eduites de la valeur absolue sur K.

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Laurent Moret-Bailly. 2010-10-02. Un th\'eor\`eme de l'application ouverte sur les corps valu\'es alg\'ebriquement clos. https://arxiv.org/abs/1010.0341

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