Forms of an affinoid disc and ramification

Schmidt, Tobias

doi:10.5802/aif.2957

Forms of an affinoid disc and ramification
[Formes d’un disque affinoïde et ramification]

Schmidt, Tobias ¹

¹ Institut für Mathematik Humboldt-Universität zu Berlin Rudower Chaussee 25, D-12489 Berlin (Germany)

Annales de l'Institut Fourier, Tome 65 (2015) no. 3, pp. 1301-1347.

Résumé
Abstract

Soit $k$ un corps non archimédien complet et soit $X$ un disque $k$ -affinoïde fermé. Nous classifions les formes modérément ramifiées de $X$ . Nous généralisons quelques résultats classiques de P. Russell sur les formes inséparables d’une droite affine et nous construisons des familles explicites des formes sauvagement ramifiées de $X$ . Finalement, nous déterminons le groupe des classes et le groupe de Grothendieck de quelques formes de $X$ .

Let $k$ be a complete nonarchimedean field and let $X$ be an affinoid closed disc over $k$ . We classify the tamely ramified twisted forms of $X$ . Generalizing classical work of P. Russell on inseparable forms of the affine line we construct explicit families of wildly ramified forms of $X$ . We finally compute the class group and the Grothendieck group of forms of $X$ in certain cases.

DOI : 10.5802/aif.2957

Classification : 14G22, 13B02, 16W70
Keywords: twisted form, affinoid disc, ramification
Mot clés : form twisté, disque affinoïde, ramification

Affiliations des auteurs :

Schmidt, Tobias ¹

¹ Institut für Mathematik Humboldt-Universität zu Berlin Rudower Chaussee 25, D-12489 Berlin (Germany)

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Schmidt, Tobias. Forms of an affinoid disc and ramification. Annales de l'Institut Fourier, Tome 65 (2015) no. 3, pp. 1301-1347. doi : 10.5802/aif.2957. https://aif.centre-mersenne.org/articles/10.5802/aif.2957/

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