Forms of an affinoid disc and ramification

Schmidt, Tobias

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

Schmidt, Tobias

Annales de l'Institut Fourier, Tome 65 (2015), p. 1301-1347 / Harvested from Numdam

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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.

Publié le : 2015-01-01
DOI : https://doi.org/10.5802/aif.2957
Classification: 14G22, 13B02, 16W70
Mots clés: form twisté, disque affinoïde, ramification

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     author = {Schmidt, Tobias},
     title = {Forms of an affinoid disc and ramification},
     journal = {Annales de l'Institut Fourier},
     volume = {65},
     year = {2015},
     pages = {1301-1347},
     doi = {10.5802/aif.2957},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2015__65_3_1301_0}
}

Schmidt, Tobias. Forms of an affinoid disc and ramification. Annales de l'Institut Fourier, Tome 65 (2015) pp. 1301-1347. doi : 10.5802/aif.2957. http://gdmltest.u-ga.fr/item/AIF_2015__65_3_1301_0/

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