First and second K-groups of an elliptic curve over a global field of positive characteristic
Annales de l'Institut Fourier, Volume 68 (2018) no. 5, pp. 2005-2067.

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.

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.

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DOI: 10.5802/aif.3202
Classification: 11R58, 14F42, 19F27, 11G05
Keywords: K-theory, function field, elliptic curve, motivic cohomology
Mot clés : K-théorie, corps de fonctions, courbe elliptique, cohomologie motivique

Kondo, Satoshi 1, 2; Yasuda, Seidai 3

1 Kavli Institute for the Physics and Mathematics of the Universe University of Tokyo 5-1-5 Kashiwanoha Kashiwa, 277-8583 (Japan)
2 National Research University Higher School of Economics Usacheva St., 7, Moscow 119048 (Russia)
3 Department of Mathematics, Osaka University Toyonaka, Osaka 560-0043 (Japan)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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, Volume 68 (2018) no. 5, pp. 2005-2067. doi : 10.5802/aif.3202. https://aif.centre-mersenne.org/articles/10.5802/aif.3202/

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