Let be a complete nonarchimedean field and let be an affinoid closed disc over . We classify the tamely ramified twisted forms of . Generalizing classical work of P. Russell on inseparable forms of the affine line we construct explicit families of wildly ramified forms of . We finally compute the class group and the Grothendieck group of forms of in certain cases.
Soit un corps non archimédien complet et soit un disque -affinoïde fermé. Nous classifions les formes modérément ramifiées de . 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 . Finalement, nous déterminons le groupe des classes et le groupe de Grothendieck de quelques formes de .
Revised:
Accepted:
Published online:
Classification: 14G22, 13B02, 16W70
Keywords: twisted form, affinoid disc, ramification
@article{AIF_2015__65_3_1301_0, author = {Schmidt, Tobias}, title = {Forms of an affinoid disc and ramification}, journal = {Annales de l'Institut Fourier}, pages = {1301--1347}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {65}, number = {3}, year = {2015}, doi = {10.5802/aif.2957}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2957/} }
TY - JOUR TI - Forms of an affinoid disc and ramification JO - Annales de l'Institut Fourier PY - 2015 DA - 2015/// SP - 1301 EP - 1347 VL - 65 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2957/ UR - https://doi.org/10.5802/aif.2957 DO - 10.5802/aif.2957 LA - en ID - AIF_2015__65_3_1301_0 ER -
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. https://aif.centre-mersenne.org/articles/10.5802/aif.2957/
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