First and second K-groups of an elliptic curve over a global field of positive characteristic  [ Sur les premier et second K-groupes d’une courbe elliptique sur un corps global de caractéristique positive ]
Annales de l'Institut Fourier, Tome 68 (2018) no. 5, p. 2005-2067
On démontre que les plus grands sous-groupes divisibles desgroupes K 1 et K 2 d’une courbe elliptique E sur un corps global de caractéristique positive sont uniquement divisibles et on décrit explicitement les K-groupes modulo leurs plus grands sous-groupes divisibles. On calcule également la cohomologie motivique du modèle minimal de E qui est une surface elliptique sur un corps fini.
In this paper, we show that the maximal divisible subgroup of groups K 1 and K 2 of an elliptic curve E over a function field is uniquely divisible. Further those K-groups modulo this uniquely divisible subgroup are explicitly computed. We also calculate the motivic cohomology groups of the minimal regular model of E, which is an elliptic surface over a finite field.
Reçu le : 2011-03-04
Révisé le : 2016-10-27
Accepté le : 2017-11-14
Publié le : 2018-11-23
DOI : https://doi.org/10.5802/aif.3202
Classification:  11R58,  14F42,  19F27,  11G05
Mots clés: K-théorie, corps de fonctions, courbe elliptique, cohomologie motivique
@article{AIF_2018__68_5_2005_0,
     author = {Kondo, Satoshi and Yasuda, Seidai},
     title = {First and second $K$-groups of an elliptic curve over a global field of positive characteristic},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {68},
     number = {5},
     year = {2018},
     pages = {2005-2067},
     doi = {10.5802/aif.3202},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2018__68_5_2005_0}
}
Kondo, Satoshi; Yasuda, Seidai. First and second $K$-groups of an elliptic curve over a global field of positive characteristic. Annales de l'Institut Fourier, Tome 68 (2018) no. 5, pp. 2005-2067. doi : 10.5802/aif.3202. https://aif.centre-mersenne.org/item/AIF_2018__68_5_2005_0/

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