Forms of an affinoid disc and ramification
Annales de l'Institut Fourier, Volume 65 (2015) no. 3, pp. 1301-1347.

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.

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.

DOI: 10.5802/aif.2957
Classification: 14G22, 13B02, 16W70
Keywords: twisted form, affinoid disc, ramification
Mot clés : form twisté, disque affinoïde, ramification
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, Volume 65 (2015) no. 3, pp. 1301-1347. doi : 10.5802/aif.2957. http://www.numdam.org/articles/10.5802/aif.2957/

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