First and second <span class="mathjax-formula">$K$</span>-groups of an elliptic curve over a global field of positive characteristic

Kondo, Satoshi; Yasuda, Seidai

doi:10.5802/aif.3202

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 ]

Kondo, Satoshi ; Yasuda, Seidai

Annales de l'Institut Fourier, Tome 68 (2018) no. 5, pp. 2005-2067.

Résumé
Abstract

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 : 2011-03-03
Révisé le : 2016-10-26
Accepté le : 2017-11-13
Publié le : 2018-11-22

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 <span class="mathjax-formula">$K$</span>-groups of an elliptic curve over a global field of positive characteristic},
     journal = {Annales de l'Institut Fourier},
     pages = {2005--2067},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {68},
     number = {5},
     year = {2018},
     doi = {10.5802/aif.3202},
     language = {en},
     url = {archive.numdam.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. http://archive.numdam.org/item/AIF_2018__68_5_2005_0/

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